# Sh:954

- Farah, I., & Shelah, S. (2010).
*A dichotomy for the number of ultrapowers*. J. Math. Log.,**10**(1-2), 45–81. arXiv: 0912.0406 DOI: 10.1142/S0219061310000936 MR: 2802082 -
Abstract:

We prove a strong dichotomy for the number of ultrapowers of a given model of cardinality \le c associated with nonprincipal ultrafilters on \mathbb{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 - Version 2010-11-24_11 (35p) published version (37p)

Bib entry

@article{Sh:954, author = {Farah, Ilijas and Shelah, Saharon}, title = {{A dichotomy for the number of ultrapowers}}, journal = {J. Math. Log.}, fjournal = {Journal of Mathematical Logic}, volume = {10}, number = {1-2}, year = {2010}, pages = {45--81}, issn = {0219-0613}, mrnumber = {2802082}, mrclass = {03C20 (46L05 46M07)}, doi = {10.1142/S0219061310000936}, note = {\href{https://arxiv.org/abs/0912.0406}{arXiv: 0912.0406}}, arxiv_number = {0912.0406} }