  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.
