Assuming the negation of the continuum hypothesis, there exist elementarily equivalent C*-algebras A and B such that A^U and B^V are non-isomorphic for every pair of non-principal ultrafilters U and V on omega.
North-Holland Publishing Co., Amster- dam
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On the isomorphism problem for ultraproducts of $\mathrm{C}^*$-algebras in continuous model theory
Assuming the negation of the continuum hypothesis, there exist elementarily equivalent C*-algebras A and B such that A^U and B^V are non-isomorphic for every pair of non-principal ultrafilters U and V on omega.