Saturation and elementary equivalence of C*-algebras

Abstract

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 $CL(X)$.

36 pages. Version 4 is rewritten for clarity in several places

References in corpus (8)

• Model theoretic forcing in analysis
• Countable saturation of corona algebras
• Rigidity of continuous quotients
• Automorphisms of corona algebras, and group cohomology
• The pseudoarc is a co-existentially closed continuum
• Omitting types for infinitary [0, 1]-valued logic
• Quantifier elimination in C*-algebras
• The Countable Chain Condition for C*-Algebras

Cited by in corpus (6)

• The pseudoarc is a co-existentially closed continuum
• Fraïssé limits of C*-algebras
• Quantifier elimination in C*-algebras
• Logic and ${\mathrm{C}}^{\ast }$-algebras: set theoretical dichotomies in the theory of continuous quotients
• Corona Rigidity
• Relative commutants of strongly self-absorbing C*-algebras