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
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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