Elementary embeddings into ultrapower $\mathrm{II}_1$ factors without a UCP lift

David Gao; David Jekel

Paper

Elementary embeddings into ultrapower $\mathrm{II}_1$ factors without a UCP lift

Abstract

We show that there are

factors

and elementary embeddings

which do not lift to sequences of UCP maps, and in fact

can be chosen from any given elementary equivalence class. Furthermore, under continuum hypothesis, we show that in the sense of cardinality "most" automorphisms of a ultrapower

of a separable

factor do not lift to a sequence of UCP maps