Saturation and elementary equivalence of C*-algebras

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