Model theory of operator algebras III: Elementary equivalence and II_1 factors
Operator Algebras
2017-05-17 v1 Functional Analysis
Logic
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.
Keywords
Cite
@article{arxiv.1111.0998,
title = {Model theory of operator algebras III: Elementary equivalence and II_1 factors},
author = {Ilijas Farah and Bradd Hart and David Sherman},
journal= {arXiv preprint arXiv:1111.0998},
year = {2017}
}
Comments
16 pages