Model theory of operator algebras III: elementary equivalence and II1 factors
By Ilijas Farah, Bradd Hart, David Sherman. 2011
118 citations recorded by the source corpus.
We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II1 factors and their ultrapowers. Among other things, we show that for any II1 factor M , there are continuum many nonisomorphic separable II1 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 II1 factor such that all II1 factors embed into one of its ultrapowers.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b5da5eab8822e5bf51908aea29caa8e08b5560cd
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In Algebra and Number Theory
In Applied Mathematics
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In Mathematical Physics
Citations in the corpus
- Independence properties in subalgebras of ultraproduct II$_1$ factors (2013, background): “ebra of an arbitrary utraproduct II1 factor, then there exist “many” non-conjugate copies of Bin M? (I am grateful to N. Ozawa for pointing out to me that the answer to this problem is not known; see [FHS] for related considerations.) On the other hand, related to Theorem 2.1 above, we propose the f”
- Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “In the terminology of [41], a II1 factor N is called locally universal if every II1 factor is finitely representable in N .”