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Anglicanorum Coetibus Society Blog
News and commentary on Anglican Patrimony inside and outside the Catholic Church
A Visitor to the Ordinariate
Posted on December 23, 2018 by Foster Lerner, D.O.
'Twas the night before Christmas, and all through the parish
Not a heresy was stirring, neither subtle nor garish;
The media were pushing secular worldviews with care,
In hopes for the young people's minds to ensnare:
The children to space out on unneeded meds;
With visions of life without God in their heads;
But our parish priest rises to lead us in prayer:
"Most Beloved in Christ, be it this Christmas Eve our care
And delight to prepare us to hear once again
The message of the angels unto Bethlehem…"
And the carols and lessons all too quickly pass,
And we kneel as our celebrant says midnight Mass.
The collection is lighter than 'twas years before,
When yet we were all on the Tiber's far shore.
And then to my wandering mind doth appear
Our church as it might be had we not come here…
And gone is our rail – no more need for kneeling –
Our high altar glorious up to the ceiling
Switched out for an Ikea table (Lame!),
As our priestess shouts out from the pulpit our shame:
Her false Sermon drones, independent of the lections (!)
"…Traditionalists with disordered affections…"
I dash away! Dash away! from my dark waking dream.
Is it only a matter of time 'til the same
Awful thing happens here in our new Catholic home?
– For the news is not so good these days out of Rome.
And then in a twinkling, it felt like my head
Had been punched, so that a rich booming voice said,
"I, Saint Nicholas fought with the Arian foe.
Him I struck with this fist long-past ages ago.
Fie! Shame! I never doubted as you are now doubting –
Even now at a Mass that recalls our Lord's coming
To the Earth – that the Lord would protect us from error.
So be present in worship, and give up this terror.
His eyes were like lightning, His muscles were wiry.
His episcopal robes gleamed all golden and fiery.
On his head a great globular miter I saw
And a white beard grew down from his large squarish jaw.
His bright golden staff had two snakes wrapped around
A cross, and he said, as he thumped it to ground,
"In the East all our bishops hold staves like this one
That of old Moses used to heal Israelites undone
By the snake's bite for they looked ahead to the Cross
That the Saviour would die on to make up our loss.
In the same way, my Son, you have nothing to dread,
For already our Lord crushed the evil one's head."
And so I returned to the Mass's contemplation,
No longer distracted by fears for church and nation.
Though our pockets are poorer (most have not even buildings),
Our hearts are made purer for that we lack these things.
And although for our leaders our former pewmates mock
The Kingdom is ours: we have built on the rock.
So I can say safely, (with my End clear in sight):
"Happy Christmas to all: Things have and shall turn out all Right!"
Written by Dr. Foster Lerner of Incarnation Catholic Church in Orlando, Florida; a parish of The Personal Ordinariate of the Chair of Saint Peter © 2018.
Foster holds a Doctorate in Osteopathic Medicine from Nova Southeastern University Dr. Kiran C. Patel College of Osteopathic Medicine, and is currently pursuing post-graduate studies in medicine.
Ormond Beach, FL, USA
This entry was posted in This Week in English Catholic History, Uncategorized and tagged Christ-Mass, Christmas, English Catholic, Great Cloud of Witnesses, Hagiography, Ordinariate, Patrimony, Saints by Foster Lerner, D.O.. Bookmark the permalink.
12 thoughts on "A Visitor to the Ordinariate"
EPMS on December 23, 2018 at 9:53 am said:
I think the accusation that altar rails are gone/going from Anglican churches is inaccurate. The GIRM identifies standing as the appropriate posture for receiving Communion, and suggests remedial catechesis for those who persist in kneeling. Consequently the altar rails have been removed from virtually every Catholic church in the US, whereas kneeling remains the norm in TEC, even when the celebration is versus populum. Even if this is changing, it seems an odd target for a jab, given the "leadership" the Church has shown on this point.
Dr. Foster Lerner, D.O. on December 23, 2018 at 2:56 pm said:
That's interesting regarding the GIRM. Could you cite the passage to which you are referring about kneeling revealing a disordered misunderstanding requiring additional catechesis?
Rev22:17 on December 23, 2018 at 9:41 pm said:
Dr. Lerner,
The relevant provision is No. 160 of the General Instruction to the Roman Missal (GIRM). This is the provision as published on the Vatican's web site, with the specific text to which "EPMS" refers in bold.
160. The priest then takes the paten or ciborium and goes to the communicants, who, as a rule, approach in a procession.
The faithful are not permitted to take the consecrated bread or the sacred chalice by themselves and, still less, to hand them from one to another. The norm for reception of Holy Communion in the dioceses of the United States is standing. Communicants should not be denied Holy Communion because they kneel. Rather, such instances should be addressed pastorally, by providing the faithful with proper catechesis on the reasons for this norm.
When receiving Holy Communion, the communicant bows his or her head before the Sacrament as a gesture of reverence and receives the Body of the Lord from the minister. The consecrated host may be received either on the tongue or in the hand, at the discretion of each communicant. When Holy Communion is received under both kinds, the sign of reverence is also made before receiving the Precious Blood.
I took this text from the English translation of the GIRM on the Vatican's web site, so the phrase "in the dioceses of the United States" in the boldfaced text might seem a bit strange — but there's actually a good reason for it. Prior to the most recent revision of the Roman Missal, the liturgical adaptations approved by national or regional episcopal conferences appeared as an appendix to the GIRM in the liturgical books for the respective country or region — but that arrangement proved to be difficult, as people preparing liturgical celebrations had to cross-reference the affected provision of the GIRM to the corresponding adaptation in the appendix. Thus, the present edition incorporates the adaptations into the respective numbered sections, usually in separate paragraphs containing a clear identifying clause ("in the dioceses of "). However, the United States Conference of Catholic Bishops (USCCB) has access to the most extensive network of theological advisors of any episcopal conference, partly because it is one of the largest and partly because many of its dioceses have plenty of resources to send clergy to study for pontifical degrees beyond the Master of Divinity (that is, doctorate or licentiate in the sacred disciplines). Many smaller episcopal conferences lack such resources, and thus find it expedient simply to adopt the adaptations approved by the USCCB for their regions as well. This practice also allows their countries or regions to use the liturgical books published for the dioceses of the United States rather than publishing their own liturgical books, which would be considerably more costly due to the small volume that they require. As a result, the adaptations indicated as applying to the dioceses of the United States actually are far more universal than such indication would imply.
JR on December 23, 2018 at 11:20 pm said:
With due respect to Norm's research, the GIRM actually found in the Missal currently in use differs from what he wrote as 'published on the Vatican's website', reflecting the Instruction, Redemptionis Sacramentum. Basically it says that the communicant simply has the option to stand or kneel when receiving and has the further option to receive either on the tongue or in the hand. There is no reference to the need for 'catechesis.' This is what the Missal says:
GIRM
160. The Priest then takes the paten or ciborium and approaches the communicants, who usually come up in procession.
It is not permitted for the faithful to take the consecrated Bread or the sacred chalice by themselves and, still less, to hand them on from one to another among themselves. The norm established for the Dioceses of the United States of America is that Holy Communion is to be received standing, unless an individual member of the faithful wishes to receive Communion while kneeling (Congregation for Divine Worship and the Discipline of the Sacraments, Instruction Redemptionis Sacramentum, March 25, 2004, no. 91).
91. In distributing Holy Communion it is to be remembered that "sacred ministers may not deny the sacraments to those who seek them in a reasonable manner, are rightly disposed, and are not prohibited by law from receiving them."177 Hence any baptized Catholic who is not prevented by law must be admitted to Holy Communion. Therefore, it is not licit to deny Holy Communion to any of Christ's faithful solely on the grounds, for example, that the person wishes to receive the Eucharist kneeling or standing.
[The footnote referred to, 177, is: Code of Canon Law, can. 843 §1; cf. can. 915.]
Regarding "The accusation" that is not an accusation: that portion of the parody is a fantasy of what "might be". No accusation was intended. Not all former Anglicans/Episcopalians/Methodists come out of TEC, you know. *I* didn't personally. Neither can anyone tell or foretell what the future or alternate timelines might hold. It also bears mentioning that another option instead of "coming here" would be joining a Novus Ordo parish, where they do indeed stand. The point rather is that Christ is in control and shall work out all things for the good of those who love Him.
The beauty of controversy is that although one may get some egg on his face, he's usually bound to learn something interesting. After researching this claim "The GIRM identifies standing as the appropriate posture for receiving Communion, and suggests remedial catechesis for those who persist in kneeling" I found its basis is in paragraph 160. of the GIRM provided by the Vatican (not as provided by USCCB which interestingly omits the relevant sentence). When I have access to my Divine Worship: The Missal, I will examine the rubrical directory to see what relevance, if any, this norm implies for the Ordinariates. Certainly, legally speaking, the Ordinariates enjoy a unique place within the Latin Rite, and it would be naïve to assume provisions of the GIRM either of Rome or of the USCCB automatically apply.
Dr. Foster Lerner, D.O. on December 23, 2018 at 10:13 pm said:
Well the rubrical directory yielded nothing in particular on the topic of kneeling at communion. However paragraph 10. reads thus: "The rubrics of the Divine Worship order of mass aim to preserve traditional customs of Anglican Eucharistic worship with respect to orientation, posture, gestures, and manual acts, while also permitting the celebration of mass in a manner similar to that of the Roman Missal, Third Typical Edition." Thus, it seems to me, since we knelt at communion when we were Anglicans out of communion with Rome, we are free and encouraged to continue this "posture" in accordance with the Rubrical Directory of Divine Worship: The Missal paragraph 10. regardless of the catechesis (on why kneeling to receive our Lord body, blood, soul and divinity is no longer an optimal way to receive him as it was in the Roman Rite for centuries and centuries prior to 1970) Rome wishes to impose on the Faithful lacking Anglican roots.
Rocky Mountain Canary on December 24, 2018 at 12:41 am said:
Jimmy Akin of Catholic Answers has a nice video about this issue, specifically how the "proper catechesis" line has in fact been excised from the norms: https://youtu.be/ave2dmAWEF8
JR on December 27, 2018 at 4:32 pm said:
As per what I quoted above.
EPMS on December 24, 2018 at 12:15 pm said:
About half ot the Catholic worship spaces shared by OCSP congregations have no altar rails. Another three or four groups use other spaces without them. Of course one can still kneel without a rail.
It is true: We are blessed at Incarnation Catholic Church in Orlando, FL both to have our own building and altar rails. May all the Ordinariate's parishes and communities in formation soon achieve the same.
This case against Catholics who tried to kneel to receive Communion went all the way to the Supreme Court of Canada https://scc-csc.lexum.com/scc-csc/scc-csc/en/item/34/index.do . One of the defendants was a lawyer and handled the case for the accused but I can'r imagime how much the Catholic diocese must have spent on the other side.


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Tag Archives: Iggy Azalea
VIDEO: @PRIDESband – Mixtape 2014 Live (You're gonna want to watch this)
Back in January I wrote about the Scottish synth-pop band Prides and now the trio has outdone themselves with this year end compilation of their favorite radio songs from 2014. Give a watch and listen to them pull off their versions of hits from 2014 which include Ariana Grande ft The Weeknd – Love Me Harder, Ryn Weaver – OctaHate, The 1975 – Settle Down, Ella Henderson – Ghost, Catfish and the Bottlemen – Cocoon, Taylor Swift – Out of the Wood, Nick Jonas – Jealous, Iggy Azalea ft Charli XCX – Fancy, Jessie Ware – Tough Love, and Sam Smith – Stay With Me.
Tags: Ariana Grande, Best of 2014, Catfish and The Bottlemen, Charli XCX, Cocoon, Covers, Ella Henderson, Fancy, Ghost, Iggy Azalea, Jealous, Jessie Ware, Love Me Harder, Mixtape, Nick Jonas, OctaHate, Out of the Wood, Prides, Remix, Ryn Weaver, Sam Smith, Settle Down, Songs, Stay With Me, Taylor Swift, The 1975, The Weeknd, Tough Love, video
2015 GRAMMY Nominations
The 2015 GRAMMY nominations were announced this morning. Take a look below at the nominees and visit GRAMMY.com for more details or peep HERE for more from Billboard.
Best New Artist
Brandy Clark
Record of the Year
"Fancy," Iggy Azalea ft. Charli XCX
"Chandelier," Sia
"Stay With Me (Darkchild Version)," Sam Smith
"Shake It Off," Taylor Swift
"All About That Bass," Meghan Trainor
"Take Me to Church," Hozier
Best Rap Performance
"305," Childish Gambino
"0 to 100/The Catch Up," Drake
"Rap God," Eminem
"i," Kendrick Lamar
"All I Need Is You," Lecrae
Best Alternative Music Album
This Is All Yours, alt-J
Reflektor, Arcade Fire
Melophobia, Cage the Elephant
St. Vincent, St. Vincent
Lazaretto, Jack White
Best Rock Album
Ryan Adams, Ryan Adams
Morning Phase, Beck
Turn Blue, The Black Keys
Hypnotic Eye, Tom Petty & the Heartbreakers
Songs of Innocence, U2
Best Rock Song
"Ain't It Fun," Paramore
"Blue Moon," Beck
"Fever," The Black Keys
"Gimme Something Good," Ryan Adams
Best Country Album
Riser, Dierks Bentley
The Outsiders, Eric Church
The Way I'm Livin', Lee Ann Womack
12 Stories, Brandy Clark
Platinum, Miranda Lambert
"American Kids," Kenny Chesney
"Automatic," Miranda Lambert
"Give Me Back My Hometown," Eric Church
"I'm Not Gonna Miss You," Glen Campbell
"Meanwhile Back at Mama's," Tim McGraw ft. Faith Hill
Best Pop Vocal Album
Ghost Stories, Coldplay
Bangerz, Miley Cyrus
My Everything, Ariana Grande
Prism, Katy Perry
x, Ed Sheeran
In the Lonely Hour, Sam Smith
Best Urban Contemporary Album
Sail Out, Jhene Aiko
Beyonce, Beyonce
X, Chris Brown
Mali Is, Mali Music
G I R L, Pharrell Williams
Best Compilation Soundtrack for Visual Media
Get On Up: The James Brown Story
Best Pop Solo Performance
"All of Me," John Legend
"Stay With Me," Sam Smith
"Happy," Pharrell Williams
Best Reggae Album
Ziggy Marley, Fly Rasta
Lee "Scratch" Perry, Back on the Controls
Sean Paul, Full Frequency
Shaggy, Out of Many, One Music
Sly & Robbie & Spicy Chocolate, The Reggae Power
Soja, Amid the Noise and the Haste
Best Traditional Pop Vocal Album
Cheek to Cheek, Lady Gaga & Tony Bennett
Sending You a Little Christmas, Johnny Mathis
Nostalgia, Annie Lennox
Partners, Barbra Streisand
Night Songs, Barry Manilow
Best Americana Album
The River & The Thread, Rosanne Cash
Terms of My Surrener, John Hiatt
Bluesamericana, Keb' Mo'
A Dotted Line, Nickel Creek
Metamodern Sounds in Country Music, Sturgill Simpson
Tags: Alt-J, Annie Lennox, Arcade Fire, Ariana Grande, Barbara Streisand, Barry Manilow, Bastille, Beck, Beyonce, Brandy Clark, Cage the Elephant, Charli XCX, Childish Gambino, Chris Brown, Coldplay, Dierks Bentley, Drake, Ed Sheeran, Eminem, Eric Church, Faith Hill, Glen Campbell, Haim, Hozier, Iggy Azalea, Jack White, Jhene Aiko, Katy Perry, Kendrick Lamar, Kenny Chesney, Lady Gaga, Lecrae, Lee Ann Womack, Mali Music, Meghan Trainor, Miley Cyrus, Miranda Lambert, Nickel Creek, Paramore, Pharrell, Pharrell Williams, Ryan Adams, Sam Smith, Sia, St. Vincent, Taylor Swift, The Black Keys, Tim McGraw, Tom Petty, Tony Bennett, U2
DoYouHearTheMusic.com June Tunes
Been a bit since I put together a playlist so here's a extended one for June. Hope you find some good tunes to rock out to.
Tags: Aer, Americna Authors, Arty, Asgeir, Avicii, Baywood, Black Lips, Boy & Bear, Calvin Harris, Chromeo, Clean Bandit, Coldplay, David Guetta, Dillon Francis, DJ Snake, Duke Dumont, Echosmith, Ed Sheeran, Empire of the Sun, Flight of Ryan, Foxes, Galantis, Ghost Beach, Gorgon City, Hardwell, Hozier, Iggy Azalea, In The Valley Below, Jake Bugg, Joywave, Jukebox the Ghost, Jungle, Jus Now, Knox Hamilton, KOPPS, Kyler England, London Grammar, Lucius, M4SONIC, MAKJ, Matthew Koma, Milky Chance, MNEK, Mystery Skulls, NO, Oh Honey, Opus Orange, Paolo Nutini, Real Estate, Route 94, Showtek, St. Vincent, Stop Dead, Strange Talk, The Chain Gang of 1974, The Orwells, Tiesta, Tove Lo, Tritonal, Typhoon, U.S. Royalty, Ummet Ozcan, Vacationer, Waka Flocka Flame, Waters, Wolf Gang, Young Empires, Young Rising Sons
Categories Music You Should Know, New Music, Playlists

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\section{Introduction}

We recall some definitions and known facts about the notion of {\em Gromov hyperbolicity}. We refer to \cite[Section 6.2]{Roe} and \cite[Section 3]{Bonk} for detailed exposition.

Let $(X,d)$ be a metric space with a fixed basepoint $x_0\in X$. For any $x,y\in X$ we denote by $(x|y)_{x_0}$ the {\em Gromov product} of $x$ and $y$ with respect to the basepoint $x_0$ defined by the following formula:
\begin{equation}
(x|y)_{x_0}=\frac{1}{2}\left(d(x,x_0)+d(y,x_0)-d(x,y)\right).
\end{equation}
\begin{deff}\label{hd}
We say that a space $X$ is $\delta$-{\em hyperbolic} for $\delta\geq 0$ if and only if
\begin{equation}\label{hyp}
(x|z)_{x_0}\geq \min \{(x|y)_{x_0},(y|z)_{x_0}\}-\delta
\end{equation}
for any $x,y,z\in X$ and for any choice of a basepoint $x_0\in X$.
We call $X$ (Gromov) {\em hyperbolic} if there exists $\delta\geq 0$ such that $X$ is $\delta$-hyperbolic.
\end{deff}

It can be shown that if a space satisfies \eqref{hyp} for a fixed $x_0$, then it is $2\delta$-hyperbolic. Thus, in the case $\delta=0$ the condition defining $0$-hyperbolicity does not depend on the choice of a basepoint and we will omit it in the notation writing simply $(x|y)$ for the Gromov product.

Bonk and Schramm showed in \cite[Theorem 4.1]{Bonk} that any $\delta$-hyperbolic metric space can be isometrically embedded into a complete $\delta$-hyperbolic geodesic metric space.
For geodesic metric spaces there is a characterisation of hyperbolicity due to Rips using so called {\em thin triangles}. As we restrict our attention to the case $\delta=0$, a geodesic metric space is $0$-hyperbolic if and only if it is uniquely geodesic and for any $x,y,z\in X$ the geodesic $[x,y]$ is contained in the union
$[x,z]\cup [z,y]$. Such spaces are called $\mathbb{R}$-{\em trees}.

Summarising, $0$-hyperbolic spaces are precisely subspaces of $\mathbb{R}$-trees. We prefer the term ``$0$-hyperbolic'' because our arguments will not depend on existence of geodesics, solely on the Gromov condition \eqref{hyp} for $\delta=0$.

\begin{deff}\label{ud}
We call a metric space $(X,d)$ $D$-{\em discrete} if $d(x,y)\geq D$ for all $x\neq y$, $x,y\in X$. If there exists $D>0$ such that $X$ is $D$-discrete, we say that $X$ is {\em uniformly discrete}.
\end{deff}

\begin{ex}
Each free group $\mathbb{F}_n$ on $n$ generators equipped with the usual word length metric becomes a $1$-discrete $0$-hyperbolic space. If we consider the Cayley graph of $\mathbb{F}_n$ with its edges realized as isometric copies of the unit interval $[0,1]$, we get a geodesic $0$-hyperbolic space (losing uniform discreteness).
\end{ex}

We wil need some useful definitions.

\begin{deff}\label{ub}
We say that a non-empty family $\mathcal{U}$ of metric spaces is {\em uniformly bounded} if the number
$$\mathrm{mesh}(\mathcal{U}):=\sup \{\mathrm{diam}(U) \colon U \in \mathcal{U}\}$$
is finite. Let $R>0$, we say that $\mathcal{U}$ is $R$-{\em disjoint} if for any different $A,B\in \mathcal{U}$ we have
$$\mathrm{dist}(A,B):=\inf \{d(a,b)\colon a\in A, b\in B\} \geq R.$$
\end{deff}

Let us recall the definition of the asymptotic property C, which was introduced by Dranishnikov \cite{Dran}. It is one of several possible generalizations of the {\em asymptotic dimension}.

\begin{deff}
We say that a metric space $X$ has the {\em asymptotic property C} if for any strictly increasing sequence $(a_i)_{i\in \mathbb{N}}$ of natural numbers there is $n\in \mathbb{N}$ and a finite sequence $\{\mathcal{U}_i\}_{i=1}^{n}$ of uniformly bounded families such that $\bigcup_{i=1}^{n} \mathcal{U}_i$ covers $X$ and $\mathcal{U}_i$ is $a_i$-disjoint for $i=1,\dots,n$.
\end{deff}

T. Radul showed in \cite{Rad} that the asymptotic property C can be thought of as a transfinite extension of asymptotic dimension.
T. Yamauchi in his paper \cite{Y} proved that the group $\bigoplus_{i=1}^{\infty} \mathbb{Z}$ with a proper invariant metric has asymptotic property C.
Our goal is to extend this result to a more general context replacing each copy of $\mathbb{Z}$ with a $0$-hyperbolic space, all of them being $D$-discrete with common $D>0$. Of course, we have to define what {\em direct sum} means for pointed metric spaces (not necessarily groups) and choose a metric such that succeeding spaces are rescaled with multipliers tending to infinity.

\section{Some auxiliary facts}

We will restate some properties of $0$-hyperbolic spaces. They are essential for a proof that such spaces have asymptotic dimension at most $1$ (see \cite[Proposition 9.8]{Roe}).

From now, let $X$ be a $0$-hyperbolic space with a fixed basepoint $x_0\in X$. For real numbers $\alpha < \beta$ we define the {\em interval} $[\alpha,\beta)\subset X$ by the formula
$$[\alpha,\beta)=\{x\in X \colon \alpha \leq d(x,x_0) < \beta\}.$$
Note that we allow $\alpha,\beta$ to be negative, in particular the interval may be empty. It will not bother us and will be useful for keeping some notation concise.
Fix $\alpha \in\mathbb{R}$ and $d,r>0$. Let us define an equivalence relation $\sim_{\alpha,r}$ in $[\alpha,\alpha+d)$ putting
$$x\sim_{\alpha,r} y \Longleftrightarrow (x|y) > \alpha - \frac{1}{2}r$$
for any $x,y\in [\alpha,\alpha+d)$. We will briefly verify that this relation is reflexive and transitive.
We have $(x|x)=d(x,x_0)\geq \alpha > \alpha - \frac{1}{2}r$ for $x\in [\alpha,\alpha+d)$.
Transitivity follows immediately from the definition of a $0$-hyperbolic space.

\begin{lem}\label{0h}
All equivalence classes of the relation $\sim_{\alpha,r}$ in $[\alpha,\alpha+d)$ are uniformly bounded by $2d+r$. Different equivalence classes are $r$-disjoint.
\end{lem}

\begin{proof}
Assume that $x\sim_{\alpha,r}y$. Then $(x|y)>\alpha-\frac{1}{2}r$, so $d(x,x_0)+d(y,x_0)-d(x,y)>2\alpha-r$. Thus
$$d(x,y)< d(x,x_0)+d(y,x_0)-2\alpha+r<2(\alpha+d)-2\alpha+r=2d+r.$$
Suppose now that $d(x,y)<r$. Then $(x|y)> \frac{1}{2}(2\alpha-r)=\alpha-\frac{1}{2}r$, which means that $x$ and $y$ belong to the same equivalence class.
\end{proof}

Observe that our result applies for all intervals $[\alpha,\alpha+d)$ and the bound $2d+r$ as well as the ``disjointness" constant $r$ do not depend on $\alpha$. Moreover, they do not depend on a particular $0$-hyperbolic space $X$.
Equivalently we can say that for any $0$-hyperbolic $X$ and $d>0$ the family $\{[\alpha,\alpha+d)\colon \alpha\in \mathbb{R}\}$ has asymptotic dimension $0$ {\em uniformly} with {\em type function} $\tau(r)=2d+r$. We refer to \cite[Example 9.14]{Roe} for the terminology.

Suppose we are given a number $R>0$. Let us consider the following families:
\begin{equation}\label{V}
\begin{split}
\mathcal{V}_0 & =  \bigcup_{n\in\mathbb{N}} [(2n-1)R,2nR)/\sim_{(2n-1)R,R},\\
\mathcal{V}_1 & =  \bigcup_{n\in\mathbb{N}_0} [2nR,(2n+1)R)/\sim_{2nR,R}.
\end{split}
\end{equation}
Both families $\mathcal{V}_0$ and $\mathcal{V}_1$ are $R$-disjoint. If two members of a fixed $\mathcal{V}_i$ are contained in different intervals, then it is easy to see that their distance is not less than $R$. For different members lying in the same interval we apply Lemma \ref{0h}.
Using Lemma \ref{0h} we also conclude that both families are uniformly $3R$-bounded. Obviously $\bigcup (\mathcal{V}_0\cup \mathcal{V}_1)=X$.

We will need some more families of subsets of $X$.
Suppose that $0<R_0<S$ and $m\in\mathbb{N}$ are given. For any $l\in\{0,\dots,2^m-1\}$ define
\begin{equation}\label{CD}
\begin{split}
\mathcal{C}_{l} & = \bigcup_{n\in\mathbb{N}_0} [(2^m (n-1)+l)S,(2^m n+l)S-R_0)/\sim_{(2^m (n-1)+l)S,R_0},\\
\mathcal{D}_{l} & = \bigcup_{n\in\mathbb{N}_0} [(2^m n +l)S-R_0,(2^m n +l)S)/\sim_{(2^m n +l)S-R_0,2^m S-R_0}.
\end{split}
\end{equation}
Similarly, $\mathcal{C}_{l}$ is $R_0$-disjoint and uniforlmy bounded for $l\in\{0,\dots,2^m -1\}$. Furthermore, $\bigcup_{l=0}^{2^m-1} \mathcal{D}_{l}$ is $(S-R_0)$-disjoint and uniformly bounded. We have also that $\bigcup(\mathcal{C}_l \cup \mathcal{D}_l)=X$ for any $l\in\{0,\dots,2^m -1\}$.

Note that the above construction works for any $0$-hyperbolic space $X$ and the boundedness and disjointness constants of the defined families remain the same.

\section{The main result}

Suppose that we have a sequence $(X_i,d_i)_{i\in\mathbb{N}}$ of $D$-discrete and $0$-hyperbolic spaces. Let $(o_i)_{i\in\mathbb{N}}$ be a sequence of basepoints $o_i\in X_i$. Define the {\em direct sum}
$$\bigoplus_{i=1}^{\infty} X_i= \left\{(x_i)\in \prod_{i=1}^{\infty} X_i \colon x_i=o_i \, \text{for all but finitely many} \, i\right\}.$$
We equip $\bigoplus_{i=1}^{\infty} X_i$ with a metric
\begin{equation}\label{metric}
d((x_i),(y_i))=\sum_{i=1}^{\infty} i\, d_i (x_i,y_i).
\end{equation}

\begin{tw}\label{main}
The metric space $\bigoplus_{i=1}^{\infty} X_i$ has asymptotic property C.
\end{tw}

\begin{proof}
The general idea is to rewrite Yamauchi's proof (\cite{Y}) replacing original families of subsets of $\mathbb{Z}$ with families \eqref{V}, \eqref{CD} of subsets of $X_i$ for $i\in\mathbb{N}$. The families will depend on $i$, which will be denoted by a superscript $(i)$. Nevertheless, the constants of disjointness and boundedness will suit for all $i\in\mathbb{N}$ uniformly. Without loss of generality we may assume that $D=1$, i.e. all the spaces $X_i$ are $1$-discrete.

Let $R_0<R_1<\dots$ be an arbitrary increasing sequence of natural numbers. Let $k=R_0+1$, $m=R_{k2^k}+1$ and $S=R_0+R_{k2^k}$. Take a bijection $\psi\colon \{0,1,\dots,2^m -1\}\to \{0,1\}^m$.
For each $i\in\mathbb{N}$ define families $\mathcal{V}_{0}^{(i)}, \mathcal{V}_{1}^{(i)}$ of subsets of $X_i$ as in \eqref{V} with $R=R_{k2^k}$.
For each $i\in\mathbb{N}$ and $l\in\{0,1,\dots,2^m -1\}$ define similarly $\mathcal{C}_{l}^{(i)}$ and $\mathcal{D}_{l}^{(i)}$ according to \eqref{CD}.
For any $j\in\mathbb{N}$ and $l\in\{0,1,\dots,2^m -1\}$ put also
$$\mathcal{W}_{l}^{(j)}=\left\{ \prod_{i=1}^{m} V_{i} \colon V_i \in \mathcal{V}_{\psi(l)_i}^{(j+i-1)}, i\in\{1,\dots,m\}\right\},$$
where $\psi(l)_i$ stands for the $i$-th coordinate of $\psi(l)\in\{0,1\}^{m}$.
Note that $\mathcal{W}_{l}^{(j)}$ is a family of subsets of $X_j \times \dots \times X_{j+m-1}$. Since $\mathcal{V}_{0}^{(i)}\cup \mathcal{V}_{1}^{(i)}$ covers $X_i$, we conclude that $\bigcup_{l=0}^{2^m -1} \mathcal{W}_{l}^{(j)}$ covers $X_j \times \dots \times X_{j+m-1}$ for any $j\in\mathbb{N}$.
Put
$$\mathcal{U}_0=\left\{\prod_{i=1}^{k} C_i \times W \times \prod_{i>k+m} \{y_{i}\} \colon (C_1,\dots,C_k,W)\in \bigcup_{l=0}^{2^m -1} \left(\prod_{i=1}^{k} \mathcal{C}_{l}^{(i)} \times \mathcal{W}_{l}^{(k+1)}  \right), (y_i)\in\bigoplus_{i=k+m+1}^{\infty} X_i\right\}.$$

We will show that $\mathcal{U}_{0}$ is $R_0$-disjoint. The elements of $\mathcal{U}_0$ depend on $l$, a choice of $C_1,\dots,C_k,W$, and a sequence $(y_i)$.
Suppose that $A,A'$ are different members of $\mathcal{U}_{0}$. If the corresponding sequences $(y_i), (y'_i)$ are different, then $d(A,A')\geq k+m+1>R_0$, which follows from the definition of the metric \eqref{metric} and $1$-discreteness of all $X_i$.
If $l\neq l'$, then the corresponding $W$ and $W'$ are disjoint (by construction of families $\mathcal{W}_{l}^{(k+1)}$) so $d(A,A')\geq k+1>R_0$.
In the remainig case we use the fact that each $\mathcal{C}_{l}^{(i)}$ is $R_0$-disjoint.

Let us fix a bijection $\phi \colon \{1,2,...,2^k\} \to \{0,1\}^k$. For $s\in \{1,2,\dots,k\}$ and $t\in \{1,2,\dots,2^k\}$ put
\begin{equation*}
\begin{split}
&\mathcal{U}_{2^k (s-1)+t}=\left\{\prod_{i=1}^{s-1} V_i \times D_s \times \prod_{i=s+1}^{k} V_i \times W \times \prod_{i>k+m} \{y_i\}\right. \colon \\
 & \left. V_i \in \mathcal{V}_{\phi(t)_{i}}^{(i)}, i\in\{1,\dots,s-1,s+1,\dots,k\}, (D_s,W)\in \bigcup_{l=0}^{2^m -1}\left(\mathcal{D}_{l}^{(s)}\times \mathcal{W}_{l}^{(k+1)}\right), (y_i)\in \bigoplus_{i=k+m+1}^{\infty} X_i \right\}.
\end{split}
\end{equation*}

We will show that for each $j\in\{1,2,\dots,k2^k\}$ the family $\mathcal{U}_j$ is $R_{k2^k}$-disjoint, in particular $R_j$-disjoint.
The reasoning is similar to that for $\mathcal{U}_0$. Fix $s$ and $t$.
Suppose that $A,A'$ are different members of $\mathcal{U}_{2^k(s-1)+t}$. If the corresponding sequences $(y_i), (y'_i)$ are different, then $d(A,A')\geq k+m+1>R_{k2^k}$.
If $l\neq l'$, then the corresponding $D_s$ and $D'_s$ are $S-R_0=R_{k2^k}$-disjoint so $d(A,A')\geq R_{k2^k}$.
If $l$ is common for $A,A'$ and $W\neq W'$, we use $R_{k2^k}$-disjointness of $\mathcal{W}_{l}^{(k+1)}$.
In the remainig case there exists $i\in\{1,\dots,s-1,s+1,\dots,k\}$ such that $V_i \neq V'_i$ and we use $R_{k2^k}$-disjointness of $\mathcal{V}^{(i)}_{\phi(t)_{i}}$.

Let us show that $\bigcup_{j=0}^{k2^k} \mathcal{U}_{j}$ covers $\bigoplus_{i=1}^{\infty} X_i$. Let $(x_i)\in \left(\bigoplus_{i=1}^{\infty} X_i\right) \setminus \bigcup \mathcal{U}_{0}$. Since $\bigcup_{l=0}^{2^m -1} \mathcal{W}_{l}^{(k+1)}$ covers $X_{k+1} \times \dots \times X_{k+m}$, there exist $l\in\{0,\dots,2^m -1\}$ and
$W\in \mathcal{W}_{l}^{(k+1)}$ such that $(x_i)_{i=k+1}^{k+m} \in W$. Since $(x_i)\not\in\bigcup \mathcal{U}_{0}$, $(x_i)_{i=1}^{k}$ does not belong to any set of the form
$\prod_{i=1}^{k} C_i$ where $C_i \in \mathcal{C}_{l}^{(i)}$ for $i\in\{1,\dots,k\}$. Thus, there is $s\in\{1,\dots,k\}$ such that $x_s \not\in \bigcup \mathcal{C}_{l}^{(s)}$. Since $\bigcup(\mathcal{C}_{l}^{(s)} \cup \mathcal{D}_{l}^{(s)})=X_s$, there exists $D_s \in \mathcal{D}_{l}^{(s)}$ containing $x_s$.
Since $\bigcup (\mathcal{V}_{0}^{(i)} \cup \mathcal{V}_{1}^{(i)})=X_i$ for each $i$, there exists $t\in\{1,\dots,2^k\}$ such that
$(x_i)_{i=1}^{k} \in \prod_{i=1}^{k} V_i$ for some $V_i \in \mathcal{V}_{\phi(t)_{i}}^{(i)}$, $i\in\{1,\dots,k\}$.
Thus,
$$(x_i)\in \prod_{i=1}^{s-1} V_i \times D_s \times \prod_{i=s+1}^{k} V_i \times W \times \prod_{i>k+m} \{x_i\} \in \mathcal{U}_{2^k (s-1)+t}.$$

Finally, the families $\mathcal{U}_{j}$, $j=\{0,\dots,k2^k\}$ are uniformly bounded. It follows from the fact that the construction of these families involves families $\mathcal{V}_{0}^{(i)}$, $\mathcal{V}_{1}^{(i)}$, $\mathcal{C}_{l}^{(i)}$, $\mathcal{D}_{l}^{(i)}$, $\mathcal{W}_{l}^{(i)}$, which are uniformly bounded with meshes independent of $i\in\mathbb{N}$.
\end{proof}

\begin{rem}
In fact we have proved more, namely $\bigoplus_{i=1}^{\infty} X_i$ has {\em transfinite asymptotic dimension} not greater than $\omega$. For definition see \cite[Section 3]{Rad}. It follows from the fact that for fixed $R_0$ there exists a natural number $n=(R_0+1)2^{R_0+1}$ (depending only on $R_0$) such that for any sequence $R_0<R_1<\dots$ there exists a sequence $\{\mathcal{U}_i\}_{i=0}^{n}$ of uniformly bounded families such that $\bigcup_{i=0}^{n} \mathcal{U}_i$ covers $\bigoplus_{i=1}^{\infty} X_i$ and $\mathcal{U}_i$ is $R_i$-disjoint for $i=0,\dots,n$. Loosely speaking, the number of sufficiently disjoint and uniformly bounded families needed to cover the space is constant for fixed $R_0$.
\end{rem}

We apply our result to the case of free groups. In the realm of dicrete spaces we call a metric {\em proper} if all balls with respect to this metric are finite.

\begin{cor}
Let $(G_i)_{i\in \mathbb{N}}$ be a sequence of free groups of finite rank (which may depend on $i$) and $G=\bigoplus_{i=1}^{\infty} G_i$ their group-theoretical direct sum. Then $G$ equipped with any proper left-invariant metric has asymptotic property C.
\end{cor}

\begin{proof}
Let $d_i$ be the usual left-invariant word length metric in $G_i$ for $i\in \mathbb{N}$. Then each $(G_i,d_i)$ is $0$-hyperbolic and $1$-discrete. The metric $d$ defined by \eqref{metric} in $G$ is proper and left-invariant. By {Theorem \ref{main}} the space $(G,d)$ has asymptotic property C. The corollary follows from the fact that all proper left-invariant metrics on $G$ are coarsely equivalent and asymptotic property C is a coarse invariant.
\end{proof}

Roe proved in \cite{Roe2} that $\delta$-hyperbolic geodesic spaces with bounded growth have finite asymptotic dimension. This suggests posing the following problem:

\begin{pro}
Can Theorem \ref{main} be generalized to the case of $\delta$-hyperbolic spaces (with common $\delta$ and commonly bounded growth)?
\end{pro}

redpajama_set_name: RedPajamaArXiv


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Borneo is celebrated for its unexplored jungle, strange endemic wildlife and indigenous communities in shared longhouses. But it also boasts five star beach resorts, fantastic local naturist guides, private river cruises and world class diving – there's no need to rough it on this rainforest adventure. Out tailor made, luxury travel holidays in Borneo makes the most of the island's superb facilities – in order to make viewing its unsurpassed nature and wildlife just that little bit more special.


The remote, relatively un-spoilt and picturesque Karpasia Peninsula is one of the outstanding IBAs in Cyprus, qualifying as a Mediterranean Biome Site, Endemic Bird Area site and as significant for no fewer than four species of global conservation concern. Good populations of Cyprus Warbler (Sylvia melanothorax) and Cyprus Wheatear (Oenanthe cypriaca) confer Endemic Bird Area status, while similarly strong populations of Sardinian Warbler (Sylvia melanocephala), and Black-headed Bunting (Emberiza melanocephala) confer Biome site status. The qualifying breeding species of global conservation concern are the European Roller (Coracias garrulus), for which the peninsula is the second most important site in Cyprus, and the Audouin's Gull (Larus audouinii), for which the Kleides islands off the tip of the peninsula (and more recently also the islet of Lefkonisos off the peninsula's North coast) are the only breeding sites in Cyprus. There are also two qualifying migrant species of global conservation concern, both raptors: Red footed Falcon (Falco vespertinus) and Pallid Harrier (Circus macrourus). The rocky Kleides islands are also the top breeding site for Mediterranean Shag (Phalacrocorax aristotelis desmarestii) in Cyprus. The rolling hills, juniper dominated maquis and low-intensity farmland of the peninsula also provide excellent breeding habitats for Stone Curlew (Burhinus oedicnemus), Cyprus Scops Owl (Otus scops cyprius), Little Owl (Athene noctua), Black Francolin (Francolinus francolinus), Chukar partridge (Alectoris chukar) and Crested lark (Galerida cristata).
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text:
Мирон-Николай Онуфриевич Зарицкий герба Новина (21 мая 1889 — 19 августа 1961) — украинский советский учёный-математик и педагог, профессор Львовского университета, действительный член Научного общества им. Т. Шевченко (с 1927), основатель украинской математической культуры, отец деятельницы ОУН и УПА Екатерины Зарицкой. Доктор философии (1930).

Биография

Детские и школьные годы
Родился 21 мая 1889 г. в с. Могильница (Королевство Галиции и Лодомерии, Австро-Венгерская империя, ныне село в Теребовлянском районе Львовской области, Украина) в семье сельского священника о. Онуфрия Зарицкого герба Новина и его жены Марии из Слоневских. На территории Галичины семья появилась после того как дедушка Мирона Онуфриевича Иван Зарицкий участвовал в Январском восстании 1863—1864 рр. эмигрировал с территории Российской империи.

Первенец в семье, родился хилым и с детства очень часто болел, но умственно развивался очень быстро. Проявлял большой интерес к природе, очень любил цветы. Впоследствии родители его переехали в Новое Село, Подволочиского района.

К началу обучения в школе самостоятельно научился читать, писать и считать, окончил начальную школу в с. Кривое у своего деда Антона Слоневского.

В 1899 г. поступает в первый класс Бережанской гимназии. Обучение давалось очень легко — первые два класса он закончил на «отлично». В Бережанах впервые увидел большой пруд, который очень его заинтересовал, научился плавать и нырять, чем доставлял много хлопот бабушки, поэтому на третьем году обучения его перевели в Тернопольскую гимназию.

Стремясь к знаниям, парень много читает (но только то, что его интересует), работает самостоятельно, в частности над математикой, значительно опережая своих товарищей. Поэтому на многих уроках в гимназии ему было неинтересно, чего не могли понять некоторые учителя, и с того выходили часто недоразумения. После одного из таких конфликтов Мирона исключили с 5-го класса Тернопольской гимназии и он поехал домой в Новое Село, где пробыл целый год. Здесь самостоятельно упорно учился и в 1905 г. без никакой помощи подготовил и сдал экстерном с хорошими оценками экзамены за 6-й класс Тернопольскую гимназию и поступил в 7-го класса классической гимназии в Перемышле.

В Перемышльской гимназии Мирон заинтересовался греческой философией, много времени посвящает изучению греческих и латинских классиков, но произведения, включенные в программу гимназии, он изучал поверхностно, и опять были определённые конфликты. Некоторые преподаватели гимназии колебались, допускать ли его до выпускных экзаменов, а он сделал им сюрприз и все сдал на «отлично».

Студенческие годы
В 1907 г. Мирон Зарицкий поступает в Венского университета, где слушает лекции по естествознанию и философии. Как большой любитель музыки, он часто посещает в Вене концерты и оперу, тратя на билеты много денег с того, что родители высылали ему на пропитание. Это отразилось на его здоровье, и поэтому после окончания первого курса родители Мирона, увидев его таким осунувшимся, уже не пустили его больше в Вену, и он вынужден был перевестись в Львовского университета. Здесь он изучает преимущественно математические и физические дисциплины, а также продолжает заниматься философией, самостоятельно изучает французский язык.

Во Львове Мирон Зарицкий становится членом студенческого общества «Академическая община», несколько позже входит в состав «Украинского студенческого союза».

На то время ведущими математиками Львовского университета были Юзеф Пузина и Вацлав Серпинский. Под влиянием профессора Серпинский Мирон Зарицкий увлекся теорией множеств и теорией функций действительной переменной, принимал участие в математическом семинаре. Эти студенческие увлечения определили позднейшее направление его научной деятельности.

На студенческих каникулах Мирон Зарицкий часто бывал в Карпатах, где собирал растения и завел себе гербарий. Любовь к природе, к карпатским горам и лесов не покидала его на протяжении всей жизни. В 1912 г. он окончил университет, а через год составил учительский экзамен и получил звание учителя средних школ из математикы и физики.

1912—1939
Имея большой интерес к научной работе, Мирон Зарицкий, однако, как и много других ученых украинцев, в условиях Австро-венгерской монархии и межвоенной Польши не мог получить работу в высшей школе и потому начал свою работу на ниве пропаганды математических знаний в различных средних школах Галичины. Он учительствует в частных гимназиях Белза и Збаража, потом, с некоторыми перерывами в годы Первой мировой войны, в государственных гимназиях Коломыи и Тернополя (от ноября 1919 года). Уже тогда делает первые шаги в научной работе по математике (работы небольшого масштаба, в которых уже содержались элементы оригинального творчества). Через некоторое время он показал эти работы в частном порядке, по известному польскому математику, профессору Львовского университета Гуго Штайнгауз, который одобрил их и беспокоился о его переезде во Львов.

В 1925 г. переехал во Львов, где работал сначала в польской, а впоследствии в государственной украинской гимназии. Он продолжает заниматься научной работой, посещает в университете лекции по психологии и философии — профессора Казимира Твардовского, по математике — профессора Гуго Штайнгауза, по астрономии — профессора Н. Эрнста и др.

24 марта 1927 г. М. Зарицкого избирают действительным членом Научного Общества им. Т. Шевченко, и с того времени он становится активным сотрудником его математической-естественной-докторской секции. В 25-м томе «Сборника» этой секции была напечатана первая его работа «Метод внедрения доброго упорядочения в теории множеств» (1926 р.). За труд «Quelques notions fondamentales de l'Analysis Situs au point de vue de algèbre de la la logique» («Некоторые основные понятия анализа положения с точки зрения алгебры логики»), напечатанную в 9-м томе журнала «Fundamenta Mathematicae» (1927 г.), Львовский университет 25 октября 1930 г. присудил Н. А. Зарицкому ученую степень доктора философии.

В это время сблизился с выдающимися польскими математиками Г. Штейнгаузом, С. Банахом, В. Стожеком, С. Мазуром, которые работали во Львове, был принят до Львовского отдела Польского математического общества, его избирают также членом Немецкого математического общества.

Принимал участие в работе I-го польского математического съезда (Львов, 1927), где выступил с научным докладом «Когеренции и адгеренции Кантора». В 1930 г. был делегатом Научного Общества им. Т. Шевченко на И-й математический съезд Советского Союза в Харькове.

С апреля 1927 г. на юбилейном празднике математической-естественной-докторской секции Научного Общества им. Т. Шевченко, посвященном 30-летию работы секции, Мирон Зарицкий произносит доклад философского содержания «Правда, красота и математика».

Среди гимназических учеников Зарицкого был Станислав Лем, о чём польский фантаст написал в своей книге «Высокий замок».

До 1939 г. опубликовал около 20 научных трудов в львовских и иностранных изданиях и в этот период сформировался как серьёзный математик с философским уклоном.

1939—1961

После присоединения Западной Украины к СССР М. О. Зарицкий с декабря 1939 г. начинает работать во Львовском университете: в 1939—1941 г. был заместителем декана, в 1945—1947 годах — декан физико-математического факультета, руководил кафедрой теории вероятностей, а с 1948 г.— кафедрой общей математики. В этот период работал старшим научным сотрудником Львовского филиала АН УССР. В 1941 г. выступал с докладами на конференциях АН УССР и АН ГССР в Киеве и Тбилиси. 21 апреля 1945 года М. А. Зарицкому было присвоено звание профессора, а 6 июля 1946 года — присуждена ученая степень кандидата физико-математических наук.

Работу во Львовском университете Зарицкий совмещал с чтением лекций в Львовском политехническом институте (1944—1946 гг.) и в новообразованном Ужгородском университете (1950—1955 гг.), оказывая большую помощь в организации математических кафедр этого университета. В 1942—1944 гг. М. Зарицкий читал лекции по высшей математике на профессиональных технических курсах, организованных на базе Львовской политехники.

Гордостью и болью Мирона Зарицкого была единственная дочь Екатерина, впоследствии — известная деятельница ОУН, председатель подпольного Украинского Красного Креста, личная связная командира УПА Романа Шухевича, многолетний заключенный польских и советских тюрем. Её мужем стал Михаил Сорока, тоже член ОУН. Именно он основал в Воркуте подпольную организацию «ОУН-Север» и был автором гимна участников Кенгирского восстания в 1954 году — «В горячих степях Казахстана». Мирону Зарицкому с женой Владимирой пришлось воспитывать и выводить в люди внука Богдана, ныне известного львовского художника-графика, ведь родители долгие годы скитались среди сибирских снегов.

Умер Мирон Зарицкий 19 августа 1961 г., похоронен на Лычаковском кладбище в Львове.

Научные интересы
Научные интересы М. О. Зарицкого охватывают, главным образом, теорию множеств из алгебры логики и теорию функций действительной переменной. Он исследует производные множества методами алгебры логики, исходя только из нескольких основных аксиом и не пользуясь другими геометрическими соображениями. Кроме того, Н. А. Зарицкий занимался теорией измеримых преобразований множеств, то есть таких гомеоморфных преобразований, которые переводят произвольное измеримое множество в другое множество такого же рода. В связи с этим он также занимался некоторыми теоретико-числовыми вопросами и напечатал статью «Некоторые числовые последовательности и их применение» (1957).

Мирон Онуфриевич был большим знатоком истории математики, особенно античной, читал курсы лекций по истории математики в Львовском университете, напечатал несколько трудов по истории точных наук. Сюда относится «Хрестоматия греческой математики» (на польском языке, 1936), в которой помещены небольшие отрывки из произведений Евклида, Архимеда, Аполлония Пергийского, Клавдия Птоломея и Диофанта в греческом оригинале и в латинском переводе, небольшой этюд «Замечания к проблеме приближенных вычислений в греческой математике» (1947), очерк «Астрономия в древности» (на польском языке, 1935).

Астрономия заинтересовала М. А. Зарицкого ещё с молодых лет. Его дядя (священник) имел большую астрономическую библиотеку; он научил Мирона Онуфриевича первых азов астрономии, возбудив интерес к глубокому изучению этого предмета. Работая в гимназиях, М. А. Зарицкий поощрял учеников к занятиям астрономией, очень часто сам ходил вечерами в астрономической обсерватории Львовского университета наблюдать звездное небо. И, уже будучи известным математиком, Мирон Онуфриевич задумал написать очерк о зарождения астрономии у древних народов Ближнего Востока. Чтобы ознакомиться с первоисточниками, ему пришлось выучить в нужном объёме древнееврейский язык.

Интересны также его очерки по методике математики в связи с историей, что печатались в польском журнале «Математика и школа».

Как философ М. О. Зарицкий интересовался теорией вероятностей и математической статистикой. Его статья «О коэффициенте корреляции в теории математической статистики» (1937) посвящена попытке анализа балансов западноукраинских кооперативов.

Будучи человеком с острым чувством общественного долга, М. О. Зарицкий проводил широкую пропаганду научных знаний в печати. Так в газетах «Дело», «Свободная Украина», «Советская Украина», «Czerwony sztandar» им было напечатано около 20 статей.

Он подготовил к печати монографию «Теория множеств», которая, к сожалению, не была напечатана, а рукопись её потерялся в стенах Львовского государственного университета им. И. Франко; перевел с французского языка на русский книгу С. Банаха «Курс функционального анализа». В украинском переводе эта книга вышла из печати в издательстве «Советская школа» в Киеве 1948 г. (через три года после смерти С. Банаха). По неизвестным причинам фамилия переводчика в книге не указано. В домашнем архиве Мирона Онуфриевича остались подготовленные к печати несколько брошюр и ряд рукописей, среди них: «Математика и формальная логика», «История античной математики», «Культурные преобразования в Западных областях УССР». Из сказанного видно, насколько разнообразны и широки были интересы ученого.

Научный вклад М. О. Зарицкого стоял на переднем крае мировой науки. На него есть ссылка, в частности, в таких известных монографиях: «К. Куратовский». Топология. — Т. 1 (М.: Мир, 1966) и Zbigniew Semadeni «Banach Spaces of continuons functions, V. I» (Warschawa; PWN, 1971). О значимости научных достижений Н. А. Зарицкого вспоминал его современник профессор Н. А. Чайковский, который писал, что об этом может свидетельствовать хотя бы тот факт, что на работы советского ученого ссылаются или цитируют их отдельные положения французские и немецкие математики Фреше и Гильберт, бывший учитель нашего земляка профессор Вацлав Серпинский и другие".

Круг интересов Мирона Онуфриевича не замыкался одной математикой. Он был знаком с естественными науками, мировой литературой, философией, увлекался поэзией. Любил Шекспира и Пушкина. Отдельные разделы поэмы Пушкина «Евгений Онегин» перевел на украинском языке. Это действительно был тип классического украинского интеллигента.

Владел свободно на польском, немецком и русском языках. Кроме того, писал математические статьи на английском, французском, итальянском и испанском языках.

Мирона Онуфриевича называли «поэтом формул». Наука у него — это творчество, вдохновение и радость, которым он хотел поделиться с каждым, кто этого желал.

Памяти

В честь математика Мирона Зарицкого и его дочери Екатерины Зарицкой в 1991 году названа улица Зарицких в Галичском районе Львов (до 1991 г. — вул. Воровского); семья Зарицких жила на этой улице в доме № 27.

Примечания

Литература
 Аксиомы для потомков: Украинские имена в мировой науке. — Зб. очерков / Под ред. А. Н. Романчука. — Львовская истор.-просвет. организ. «Мемориал», 1992. — 544 с., арк. ил. ISBN 5-8690-010-6
 «Возняк Г». Мирон Зарицкий — основатель украинской математической культуры // Математика в школе. — 1999. — № 3. — С. 53-55.
 «Кушнерик Г., Пиндус Бы.» Зарицкий Мирон Онуфриевич // Тернопольский энциклопедический словарь : в 4 т. / редкол.: Г. Яворский и др. — Тернополь : Издательско-полиграфический комбинат «Збруч», 2004. — Т. 1 : А — Й. — С. 622. — ISBN 966-528-197-6.
 «Птичник». Поэт математики // Аксиомы для потомков: Украинские имена в мировой науке. — Л., 1991. — С. 41-56.
 «Птичник». Поэт математических формул // В мире математики. — 2002. — Т. 8, вып. 4. — С. 86-91.

Ссылки
 Мирон Зарицкий
 на сайте Создатели математики с Украины

Математики СССР
Доктора философии по математике
Кандидаты физико-математических наук
Преподаватели Львовской Политехники
Преподаватели Ужгородского университета
Похороненные на Лычаковском кладбище
Математики Украины

redpajama_set_name: RedPajamaWikipedia


Estate Planning is one aspect covered when creating a financial plan. Estate planning consists of everything you own and how you want your belongings to be distributed and controlled after your death. An estate consists of your house, personal items, car, life insurance, investment options, checking and savings accounts and other real estate. Therefore, everyone has an estate. Estate planning is not something to add to your financial plan when you near death. It is something that should be part of your financial plan from the start and altered when needed because you cannot predict when you fall ill. Estate planning is not just for wealthy individuals. As a result, too many people do not plan. People put off estate planning because they think they do not have many assets, they are not old enough, they are too busy to create a plan, think they have plenty of time, they are confused on how to start a plan, and do not know who can help them, or they just do not want to think about an estate plan. Then, when something happens to them, their families are left with many unanswered questions and missing pieces. Therefore you should create a plan because estate planning allows you to control what belongings family members or charitable organizations receive after your death.
In order for estate planning to work, you need to write out instructions. These instructions should include the 3 W's: Who, What, and When; who you do you want to receive your belongings, what do you want them to receive and when you do want them to receive them. These instructions are usually left in a will. Estate planning is not just for after your death but also a plan if you become disabled. You should include instructions for care if you become disabled before you die. If you have you children they should also be included in your plan. You should name a guardian and an inheritance manager for you children. You do not want special needs family members to be left without any support. In your estate plan, you should provide for special needs family members but without interfering with government benefits. You should include life insurance, disability insurance and long-term care insurance in your plan. Life insurance will help your family financially after your death. Disability insurance will replace your income if you cannot work due to an injury or illness. Long-term care will help pay for your care in case of a long-term injury or illness. Your estate plan should also include plans for your business if you are an owner. You should provide instructions for the transfer of your business when you retire, become disabled, or die. You should consult an accountant and lawyer if minimize taxes, legal fees and court fees.
As mention before, an estate plan is ongoing. Your plan should be reviewed and altered as your family and financial situations change. If you do not create an estate plan, then the courts will have to make decisions on your behalf instead of your family. Overall, an estate plan gives you a peace of mind because you know your family will be taken care of after your death.
Below is an example of a report generated by our financial advisors. By filling out the form above, you will receive a personalized financial analysis outlining optimal financial strategies based on your goals.


Pebble Pictures - Shop Now!
Proving to be very popular are my unique pebble pictures for all occasions. They make fantastic gifts. Made from beach pebbles and drift wood primarily, have a lovely rustic feel.
- Also can be personalised with dates, names or message. Your own ideas/requests also welcome.
- White or black frame.
Extra kids can be added and personalise with your own message.
On your retirement? Happy fathers day? Happy mothers day? Happy birthday? So many to chose from.
Home sweet home? New home?


text:
Fender's 2022 launches unveiled
Epiphone Joan Jett Olympic Special
Gibson NFTs
Lord of the Rings becomes 3-hour metal song
How understanding the power of leading tones will help you craft better melodies
By Stéphane Wrembel published 31 July 20
An essential lead-writing primer with jazz guitarist Stéphane Wrembel
Both improvising and composing are states of mind, separate but with the shared goal of creating melodies. But creating melodies is a great mystery! There is no formula for it, just as there is no formula for writing a novel.
There are, however, a few tools, or devices, that we can use to make it possible to find melodic angles to the lines we construct, and one particularly useful one is the use of what is called a leading tone, also known as an approach note, which is a note one half step below the target note, which is typically the root of the chord.
The use of leading tones is something I discovered in studying the counterpoint of Renaissance music, in which it was often employed in the resolution of melodic phrases. The presence of the leading tone in setting up the return to the tonic (the "one" chord of the home key) serves to reinforce the sense of the overall tonality of the composition.
If I have a melody based on the notes of the C major scale, I can use the B note to close the phrase, reinforce the sense of tonality and create a beautiful melody, as demonstrated in FIGURE 1. The B-to-C move seems to magically reinforce the resolution to the tonic, C, and does so with a satisfying sense of finality.
In a minor key, oftentimes we will play ascending melodies using one series of notes and use a different one in descending melodies. FIGURE 2 illustrates the C melodic minor scale (C, D, Eb, F, G, A, B), which is used for ascending melodic lines, and FIGURE 3 depicts the C natural minor scale, or C Aeolian mode (C, D, Eb, F, G, Ab, Bb), which is traditionally used for descending melodic lines in the key of C minor.
The reason we use melodic minor on the way up is it includes the B natural leading tone, which makes for a more pleasing resolution. FIGURE 4 offers examples of this principle in action.
Let's now apply this principle to a 12-bar blues form in G minor. We will use the F# leading tone into G, a B leading tone into C and a C# leading tone into D. FIGURE 5 illustrates the first of two solos over this 12- bar form: here, the entire melodic content of the solo is based on moving from the leading tone to the temporary tonic, which is the underlying chord at the moment.
Next, FIGURE 6 offers another 12-bar improvised solo: here, I build more complex phrases that relate directly to each chord in the progression. Notice how I've employed arpeggios to outline, or melodically describe, the underlying chords.
It's good practice to improvise over the 12-bar minor blues form at various tempos, so record a backing track to solo over and try to infuse as many of these techniques as you can into your own creative lines.
US pricing $3.99 per month or $39.00 per year
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Prices from £2.99/$3.99/€3.49
How one man unearthed the first-ever Washburn N4 production model – and ended up selling it to Nuno Bettencourt
Marcus Miller: "I try to play from my ears and not from my fingers"
Steve Vai reveals the most difficult aspect of playing Eddie Van Halen's guitar parts
Duvoisin Standard 5 review
Harness the attitude of Johnny Winter with this lesson in his swaggering blues style


The interrupt controller is an implementation of the reference interrupt controller (see Interrupt controller).
Range:Base specifies the area in memory into which the interrupt controller registers are mapped. For details of the interrupt controller registers, see Interrupt controller.
WAITS specifies the number of wait states that accessing the interrupt controller imposes on the processor. The maximum is 30.


>> metadata front, and woefully difficult to extend.
> Would Debian's .deb format be better ?
done) instead of a CPIO archive and it would work just as well.
hierarchy in the appropriate place in the tag tree.
that there has recently been a (long necessary) fork between "community"
installations", a task that I think he relishes.
possible that yum will really move.
new beast that has it all and does it all, efficiently).
want along the way WITHOUT altering the underlying library).
distribution" by extension and hence installable in /usr).
by people who DO know better but don't care enough to do it "right"
rpmbuild, and why should they change?
that robust, best practice coding?  I call it s**t. Bloody amateur s**t.
pretty good, doesn't it?  Maybe you can think of one or two targets...?
nearly anything).  Or a whole lot better.
itself and less on rpm per se.
(usually) to make things work, they aren't as natural as one might like.


Noted Hong Kong director Johnny To creates this Chinese Western set in Macao. Lau Ching-wan plays Michael Cheung, a triad member and newly released ex-con, who is trying to track down his wife and the $2,000,000 she stole. On the way, he runs into lonely workaholic Judy (Ruby Wong), who lives with her young son. Gun-shy, the two adults slowly edge toward something like a relationship, until outside events complicate matters. Where a Good Man Goes was screened at the 1999 Pusan Film Festival.
There are no critic reviews yet for Where a Good Man Goes (Joi gin a long). Keep checking Rotten Tomatoes for updates!
There are no featured reviews for Where a Good Man Goes (Joi gin a long) at this time.


Firstly what you should not use.
Any product containing silicone. Silicone penetrates the lacquer and is still present even if the furniture is stripped back to the bare timber. Silicone prevents the lacquer from flowing either as a recoat or after stripping. The result is that the surface is riddled with small round holes going all the way back to the timber. It can be overcome but it is far easier without the silicone being there in the first place.
Any oil based product. Oil takes too long to dry and gathers airborne dust whilst drying. The next time anyone rubs the surface or applies a new coat of oil, the oil and dust form an abrasive that scratches the surface.
Wax is going to form a film on the surface. This may be a problem on a high gloss finish leaving smear marks that are very difficult to buff out. Wax can be used to help in making the surface more slippery and assist in deflecting sharp objects.
Surfaces can be cleaned with mineral turpentine or gum turpentine for oil-based dirt. Whereas a mild detergent will remove water-soluble marks. A fragrance can be added to either cleaner if required.
Crystal veneer can be used if the surface requires a very mild cut and polish to restore the shine and lustre of the finish.
Doors and drawers may stick from time to time if insufficient allowance has been made by the manufacturer for the timber's normal expansion and contraction that is due to changes in humidity.


text:
ENDAblog
A great LGBT community deserves full inclusion
About ENDA
The John Plays the Fox 'News' Game of 'Some Say…'
Not with that exact verbiage, but you'll get the idea in this excerpt from a piece about the ENDA blame game that is ramping up:
[T]here's this:
Mara Keisling, executive director of the National Center for Transgender Equality, also blamed Republicans for the failure to advance ENDA in the Senate. She also cited what she called a "general dysfunction" in the chamber as a problem.
"It's certainly not all about ENDA," she said. "It's certainly, certainly not about transgender inclusion in ENDA. They can't get campaign finance reform through, they can't get, sometimes, job bills through."
That's not what I've been hearing.
On the one hand, it truly is hard to find fault with The John for, at least on principle, not believing things that emerge from the Head Quack at the Quisling Quacktory.
On the other hand, "Thats not what I've been hearing" sounds more than a little bit like the (if it wasn't, then it should have been) patented "Some say…" trick of Fox 'News'. And, when one considers the gay-first-including-gay-marriage-and-yes-that-means-that-you'd-better-not-suggest-that-incremental-progress-applies-to-gay-marriage greed mentality of those who share space in The John's echo chamber, I can actually believe that all he's been hearing is how 'that e-vul trans-scum' is mussing up 'their' ENDA.
Meanwhile, back in reality….
1 Comment	| Action Alerts, John Aravosis, WRPGMs	| Permalink
Posted by Katrina Rose
How to Observe Day of Remembrance This Year? Help a Transphobic Gay Male Exploitation Artist Line His Diseased Pockets
I surfed over to this Fangoria page from a post by Kelli Busey – a post that I'd hoped was a satirical sequel to my Myra Breckinridge Luna-Tick post.
But, alas…
One of the most controversial films shown at New York's Tribeca Film Festival earlier this year was TICKED-OFF TRANNIES WITH KNIVES, a horror-revenge film that ticked off certain members of the transgendered community itself. Now it's poised to provoke some more, as it has a North American distributor.
Breaking Glass Pictures gave Fango the scoop that it has acquired the rights to the movie, and plans theatrical screenings during the Halloween season, followed by DVD/video-on-demand release in November.
Make sure that your community's DOR observance is the first to include a screening of a film that, whether any of the Luna-Tick's conspirators and/or apologists acknowledge it or not, is designed to encourage violence against trans women!
Appletini!
2 Comments	| Action Alerts	| Permalink
The "U.K. Buys the Janice Raymond-Consecrated Transphobia of the Michigan Womyn's Music Festival and Vancouver Rape Relief" Act of 2010
Strangely enough, that's not the official name of a recent creation of Parliament – one that makes the Gender Recognition Act of 2004 not worth the paper its printed on (and the gender recognition certificates that that 2004 act allows for worth even less than that.)
Perversely, the official name is the "Equality Act."
Here's what Zoe Brain has to say about it:
[T]here is one "protected" class where protection is explicitly removed, not granted. It means that a gender recognition certificate is not worth the paper it's printed on. Rather than being a recognition that they are of the target gender, it's a nullity, as the law states that they're not, not really. This is made clear in the explanatory notes.:
A group counselling session is provided for female victims of sexual assault. The organisers do not allow transsexual people to attend as they judge that the clients who attend the group session are unlikely to do so if a male-to-female transsexual person was also there. This would be lawful.
Schedule 9: Work: exceptions
Part 1: Occupational requirements
A counsellor working with victims of rape might have to be a woman and not a transsexual person, even if she has a gender recognition certificate, in order to avoid causing them further distress.
The provisions of the Gender Recognition Act 2004 that over-rode that 1975 act have now been repealed. There is a distinction between "women" and "transsexual persons with (or without) gender recognition certificates" now.
Okay, so Zoe and I have different qualitative assessments as to what is worth a piece of paper and what is worth less.
Nevertheless, I think we have a similarly negative assessment as to the reality of what the Anti-GRA Act is. Zoe, however, captures it more brilliantly with a comparative graphic than I can with legalese:
I think I'll give it a try…
This is an acceptable woman:
But this isn't:
It all makes perfect sense.
Where is my 'Alix Dobkin Cassette' suppository?
The Eyes of (the State Bar of) Texas Are Upon the Lawyer Who is Trying to Nullify Nikki Araguz's Marriage and Life
Lack of ethics, much? From the Houston Press:
Frank Mann, the lawyer representing Thomas Araguz's ex-wife, is facing investigation by the State Bar of Texas's disciplinary office for a possible ethics violation related to an e-mail he sent "outing" the widow, Nikki Araguz, during her mayoral campaign.
Mann represented Araguz and her first husband in a 2002 bankruptcy case. Earlier this year, he represented Heather Delgado, Thomas Araguz's ex-wife, in a bitter custody dispute, and is now representing her in a motion to void Nikki's and Thomas' 2008 marriage.
In an April deposition of Nikki Araguz, Mann got her to admit that she was born Justin Graham Purdue; he also asked about her medical history. Mann then used the information in a May 6 e-mail titled "Public Information on Nikki Araguz who is running for Mayor of Wharton, Texas."
Possible ethics violation?
And – since this blog isn't a court of law, Frank Mann's past can be brought in to convict him in the court of public opinion…
you know, the way he disclosed information about Nikki in order to sabotage her campaign? And now to sabotage her legal interests? The difference is, of course, evn though I am a lawyer, this clown wasn't my client – and I definitely didn't learn this info via attorney-client confidentiality:
It's not Mann's first dance with the Office of Disciplinary Counsel: in 1990, Mann agreed to a fully probated 36-month suspension for "misrepresentations of fact concerning the dates of his hospitalization for alcohol and substance abuse in an affidavit offered in support of a motion to retain." (The suspension was stayed; he was allowed to actively practice, but was placed on probation.) The Office of Disciplinary Counsel also ruled that, in one case, Mann "assigned away 100 percent of any attorney's fees" and then "intervened in the pending lawsuit, claiming an interest in attorney's fees."
In 1997, Mann was suspended for five and a half years and was not eligible to practice for the first 36 months. In that case, among other things, the Counsel found that Mann's paralegal "affixed [a] client's signature from a prior document to a proposed modification, without the client's consent." Mann wasn't in the office at the time, but he was "responsible supervision and instruction of his staff and for ensuring that his staff follows the law and the Texas Disciplinary Rules of Professional Conduct."
Okay – the paralegal thing doesn't necessarily call into question his honesty, just his competence at overseeing his employees.
According to Mann:
all of the information in his May 6 e-mail was gleaned from the deposition, and not from his earlier representation of Araguz and her first husband.
He also said that, when he represented Nikki Araguz in the 2002 bankruptcy, he did not know anything about her sexual identity and only focused on financial matters.
To be absolutely fair: Yes, its is possible that that is accurate.
If I can find a bookie who'll give me odds, however, I'll put $20 down against it. Sadly, I suspect the 'official' paper trail will not yield the type of dot-connecting that will force the State Bar to disbar the guy. Nevertheless, I have trouble believing that in 2002 the subject of any and all former names of a bankruptcy petitioner was never discussed during either the proceedings themselves or at some point during representation of that petitioner.
7 Comments	| Intersex, Non-ENDA	| Permalink
Christianism is as Christianism Does
Oooooooooohhhhhhhhh, but its the Kweeeeeeeeeeeerrrrrrzzzzzzzzzz who are evil, eh?
From WREG in Memphis:
Memphis city council member Janis Fullilove has received multiple death threats related to her efforts to ban discrimination against gays in city government.
Police think the threats are serious enough have increased patrols around her home to keep her safe. All four calls came Tuesday and each call mentioned the proposed employee non-discrimination ordinance. Someone also threw a dead cat on her lawn. Each phone call mentioned her support for banning discrimination against gays in city government. Distraught, Fullilove reached out to Jonathan Cole with the Tennessee Equality Project.
"She essentially said that they were threatening to kill her," said Cole, who thinks the death threats are just another example of intolerance in Memphis. "It's scary and our city needs to stand up to this kind of ugliness."
Tennessee stand up to theocratic fascists? I'm not holding my breath.
Leave a Comment »	| Random nutty fundies	| Permalink
Why Can't the MSM be This Honest and This Direct?
Oh, silly me…
Its the MSM after all. News a priority? Not over profits.
From Mike Whitney at CounterPunch:
The Conference Board's confidence index dropped to a 5-month low of 50.4 from 54.3 in June. According to Bloomberg News:
"Sentiment may be slow to improve until companies start adding to payrolls at a faster rate, and the Federal Reserve projects unemployment will take time to decline. Today's figures showed income expectations at their lowest point in more than a year, posing a risk for consumer spending that accounts for 70 per cent of the economy.
"Consumers' faith in the economic recovery is failing," said guy LeBas, chief fixed-income strategist at Janney Montgomery Scott LLC in Philadelphia, whose forecast of 50.3 for the confidence index was the closest among economists surveyed by Bloomberg. "The job market is slow and volatile, and it'll be 2013 before we see any semblance of normality in the labor market." (Bloomberg)
Confidence is falling because unemployment is soaring, because the media is lying, and because the Fed's monetary policy has failed. Notice that Bloomberg does not mention consumer worries over "curbing the deficits". In truth, the public has only a passing interest in the large deficits. It's a fictitious problem invented by rich corporatists (and their think tanks) who want to apply austerity measures so they can divert more public money to themselves. In the real world, consumer confidence relates to one thing alone–jobs. And when the jobs market stinks, confidence plummets.
How long would Brian Williams keep his job if he spoke this reality on the Help General Electric Keep Its Defense Contracts Nightly Propaganda Dose?
Leave a Comment »	| Non-ENDA	| Permalink
Why Does Anyone Interview Log Cabin Republicans About Anything?
From a Queer Channel Media piece about Joe Solmonese's toilet paper ENDA:
R. Clarke Cooper, executive director of the Log Cabin Republicans, dismissed the notion that Republicans were holding up ENDA in the Senate and said "only the current Senate majority leadership can truly answer" why ENDA isn't on the calendar.
"Blaming the minority leadership for the majority's disorganization and lack of planning this year is simplistic and, frankly, lazy," Cooper said. "Both sides of the aisle are frustrated with the lack of activity."
How about just going ahead and interviewing Tony Perkins and Lou Sheldon for some more 'balance', eh QCM? Its bad enough that QCM interviewed Quisling McNothingburger – as if that head of the Quisling Quacktory speaks for any trans lifeform outside of the Court of the Quimson Quisling – but a clown from an organization that is inherently a joke (as opposed to the Quisling Quacktory; after all, in theory, an organization with 'transgender equality' in its name only becomes a joke via Quisling Contwowl)? Is Chris Crain back on the payroll?
Leave a Comment »	| WRPGMs	| Permalink
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After graduating college in 1992 and leaving my baseball career behind, I began playing my first and only season of softball. Perhaps if the softball league had been co-ed (smile) I may have enjoyed it a little more. For me, the "soft" game lacked the competition and challenge I was accustomed to, and I assumed that my playing days were over.
Thankfully, my dad saw an ad in the Marietta Daily Journal showcasing the Atlanta Men's Adult Baseball League (MABL). Within a few days of discovering the men's league, I went to a tryout and was drafted by the MABL Cobb Cardinals. I have played every year since, and I now look forward to every Sunday afternoon game. Being on that diamond is my sanctuary.
The Atlanta MABL and MSBL (Men's Senior Baseball League) was founded in 1988 and has grown to 100+ teams. Managed from Smyrna by Donald Pike, the men's league is divided up into skill and age divisions, and all games are played on OTP High School fields throughout the area. Men compete from 18 to 65 years old in their respective divisions. The Atlanta league is affiliated with the MSBL National headquartered in New York.
The MSBL National is managed by founder Steve Sigler (father of Sopranos star Jamie-Lynn Sigler). The MSBL National has 325 local affiliates, 3,200 teams and 45,000 members who compete in their local leagues. 30 regional tournaments plus six national tournaments are also available to all of the affiliated teams and leagues. Both the MSBL and the MABL plan to expand by establishing local affiliates in communities where programs do not exist, and also by welcoming existing amateur hardball leagues to affiliate. The MSBL is poised to reach 50,000 members in the very near future.
The Atlanta men's league is run extremely well and the competition is excellent. The MABL/MSBL's season lasts the duration of the MLB season with games played on Sunday afternoons. There are also Saturday, Wednesday night, and Fall Leagues available. All of the leagues feature a playoff and championship series.
If you are interested in joining the league, go to www.atlantamsbl.com. League fees average approximately $200 for the season; you will also have some uniform and equipment costs to consider. The MABL Fall season is approaching quickly. Rediscover your youth and expand your passion for the great game of baseball. Get out there and play ball!