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arXiv · 1111.0998

Model theory of operator algebras III: Elementary equivalence and II_1 factors

Ilijas Farah·Bradd Hart·David Sherman
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Abstract

We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II_1 factors and their ultrapowers. Among other things, we show that for any II_1 factor M, there are continuum many nonisomorphic separable II_1 factors that have an ultrapower isomorphic to an ultrapower of M. We also give a poor man's resolution of the Connes Embedding Problem: there exists a separable II_1 factor such that all II_1 factors embed into one of its ultrapowers.

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Ilijas Farah, Bradd Hart, David Sherman. 2011-11-03. Model theory of operator algebras III: Elementary equivalence and II_1 factors. https://doi.org/10.1112/blms%2Fbdu012

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