  With each of the usual tree forcings I (e.g., I = Sacks forcing S, Laver
forcing L, Miller forcing M, Mathias forcing R, etc.) we associate a
sigma--ideal i^0 on the reals as follows: A \in i^0 iff for all T \in I there
is S \leq T (i.e. S is stronger than T or, equivalently, S is a subtree of T)
such that A \cap [S] = \emptyset, where [S] denotes the set of branches through
S. So, s^0 is the ideal of Marczewski null sets, r^0 is the ideal of Ramsey
null sets (nowhere Ramsey sets) etc.
  We show (in ZFC) that whenever i^0, j^0 are two such ideals, then i^0 \sem
j^0 \neq \emptyset. E.g., for I=S and J=R this gives a Marczewski null set
which is not Ramsey, extending earlier partial results by Aniszczyk,
Frankiewicz, Plewik, Brown and Corazza and answering a question of the latter.
In case I=M and J=L this gives a Miller null set which is not Laver null; this
answers a question addressed by Spinas.
  We also investigate the question which pairs of the ideals considered are
orthogonal and which are not.
  Furthermore we include Mycielski's ideal P_2 in our discussion.

Logic