|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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