  We study the saturation properties of several classes of $C^*$-algebras.
Saturation has been shown by Farah and Hart to unify the proofs of several
properties of coronas of $\sigma$-unital $C^*$-algebras; we extend their
results by showing that some coronas of non-$\sigma$-unital $C^*$-algebras are
countably degree-$1$ saturated. We then relate saturation of the abelian
$C^*$-algebra $C(X)$, where $X$ is $0$-dimensional, to topological properties
of $X$, particularly the saturation of $CL(X)$.

Logic;Operator Algebras