Forcing axioms and coronas of $C^{\ast }$-algebras

Abstract

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable $C^{\ast }$-algebras with the metric approximation property and an increasing approximate identity of projections.

arXiv comment71 pages, appeared online in Journal of Mathematical Logic (Online version)

References in corpus (10)

• Perturbations of nuclear C*-algebras
• Countable saturation of corona algebras
• Rigidity of continuous quotients
• Automorphisms of corona algebras, and group cohomology
• Perturbations of C*-algebraic invariants
• Model theory of ${\mathrm{C}}^{\ast }$-algebras
• Reduced products of UHF algebras under forcing axioms
• Nontrivial homeomorphisms of Čech-Stone remainders
• Embedding ${\mathrm{C}}^{\ast }$-algebras into the Calkin algebra
• Rigidity Conjectures

Cited by in corpus (2)

• Corona Rigidity
• The weak Extension Principle