Reduced products of UHF algebras under forcing axioms

Abstract

If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n/⨁A_n$ is called a reduced product. We prove, assuming Todorcevic's Axiom and Martin's Axiom, that every isomorphism between two reduced products of separable, unital UHF algebras must be definable in a strong sense. As a corollary we deduce that two such reduced products $\prod A_n/⨁A_n$ and $\prod B_n/⨁B_n$ are isomorphic if and only if, up to an almost-permutation of $\mathbb{N}$, $A_n$ is isomorphic to $B_n$.

31 pages

Cited by in corpus (1)

• Logic and ${\mathrm{C}}^{\ast }$-algebras: set theoretical dichotomies in the theory of continuous quotients