# Sh:954

• Farah, I., & Shelah, S. (2010). A dichotomy for the number of ultrapowers. J. Math. Log., 10(1-2), 45–81.
• 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}
}