Countable saturation of corona algebras

Abstract

We present unified proofs of several properties of the corona of $\sigma$-unital C*-algebras such as AA-CRISP, SAW*, being sub-$\sigma$-Stonean in the sense of Kirchberg, and the conclusion of Kasparov's Technical Theorem. Although our results were obtained by considering C*-algebras as models of the logic for metric structures, the reader is not required to have any knowledge of model theory of metric structures (or model theory, or logic in general). The proofs involve analysis of the extent of model-theoretic saturation of corona algebras.

To appear in Comptes Rendus Mathématiques

References in corpus (1)

• Automorphisms of corona algebras, and group cohomology

Cited by in corpus (11)

• Saturation and elementary equivalence of C*-algebras
• Logic and operator algebras
• Rigidity of continuous quotients
• Automorphisms of corona algebras, and group cohomology
• Forcing axioms and coronas of $C^{\ast }$-algebras
• Reduced products of UHF algebras under forcing axioms
• A new bicommutant theorem
• Logic and ${\mathrm{C}}^{\ast }$-algebras: set theoretical dichotomies in the theory of continuous quotients
• Corona Rigidity
• Embedding ${\mathrm{C}}^{\ast }$-algebras into the Calkin algebra
• Relative commutants of strongly self-absorbing C*-algebras