Model theory of operator algebras III: Elementary equivalence and II1 factors

Abstract

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