### A Dichotomy for the number of ultrapowers

by Farah and Shelah. [FaSh:954]

J Math Logic, 2010

We prove a strong dichotomy for the number of ultrapowers
of a given model of cardinality <= c associated with
nonprincipal ultrafilters on {N} . They are either all
isomorphic, or else there are 2^c many. We prove the
analogous result for metric structures, including
C^*-algebras and II_1 factors, as well as their relative
commutants

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