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arXiv · 1303.5037

Reduced products of UHF algebras under forcing axioms

Paul McKenney
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Abstract

If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n / \bigoplus A_n$ 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 $\prod A_n / \bigoplus A_n$ and $\prod B_n / \bigoplus B_n$ are isomorphic if and only if, up to an almost-permutation of $\mathbb{N}$, $A_n$ is isomorphic to $B_n$.

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Paul McKenney. 2013-03-20. Reduced products of UHF algebras under forcing axioms. https://arxiv.org/abs/1303.5037

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