Existentially closed II1 factors

Abstract

We examine the properties of existentially closed (Rω-embeddable) II1 factors. In particular, we use the fact that every automorphism of an existentially closed (Rω-embeddable) II1 factor is approximately inner to prove that Th(R) is not modelcomplete. We also show that Th(R) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th(R).