II1 FACTORS WITH NONISOMORPHIC ULTRAPOWERS

We prove that there exist uncountably many, separable II1,factors whose ultrapowers (with respect,to arbitrary ultrafilters) are nonisomorphic. In fact, we prove that the families of nonisomorphic II1 factors originally introduced by McDuff are such examples. This entails the existence of a continuum of nonelementarily equivalent II1 factors, thus settling a well-known open problem in the continuous model theory of operator algebras.