We prove that there exist uncountably many separable factors whose ultrapowers (with respect to arbitrary ultrafilters) are nonisomorphic. In fact, we prove that the families of nonisomorphic factors originally introduced by McDuff are such examples. This entails the existence of a continuum of nonelementarily equivalent factors, thus settling a well-known open problem in the continuous model theory of operator algebras.
"II factors with nonisomorphic ultrapowers." Duke Math. J. 166 (11) 2023 - 2051, 15 August 2017. https://doi.org/10.1215/00127094-0000017X