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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