Authors: | Farah, Ilijas Shelah, Saharon |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | A dichotomy for the number of ultrapowers | Journal: | Journal of Mathematical Logic | Volume: | 10 | Issue: | 1-2 | First page: | 45 | Last page: | 81 | Issue Date: | 1-Jun-2010 | Rank: | M23 | ISSN: | 0219-0613 | DOI: | 10.1142/S0219061310000936 | Abstract: | We prove a strong dichotomy for the number of ultrapowers of a given model of cardinality ≤ 2א0 associated with nonprincipal ultrafilters on ℕ. They are either all isomorphic, or else there are 2 2א0 many nonisomorphic ultrapowers. We prove the analogous result for metric structures, including C*-algebras and II1 factors, as well as their relative commutants and include several applications. We also show that the C*-algebra B(H) always has nonisomorphic relative commutants in its ultrapowers associated with nonprincipal ultrafilters on ℕ. |
Keywords: | Dichotomy | ultrapower | Publisher: | World Scientific | Project: | Israel Science Foundation, Grant no. 710/07 |
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