This is an announcement for the paper "A dichotomy for the number of ultrapowers" by Ilijas Farah and Saharon Shelah.
Abstract: We prove a strong dichotomy for the number of ultrapowers of a given countable model associated with nonprincipal ultrafilters on N. They are either all isomorphic, or else there are $2^{2^{\aleph_0}}$ many nonisomorphic ultrapowers. We prove the analogous result for metric structures, including C*-algebras and II$_1$ 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.
Archive classification: math.LO math.OA
Mathematics Subject Classification: 03C20, 46M07
Report Number: Shelah [FaSh:954]
The source file(s), 2009i19-ultrapowers.tex: 122804 bytes, is(are) stored in gzipped form as 0912.0406.gz with size 33kb. The corresponding postcript file has gzipped size 176kb.
Submitted from: ifarah@yorku.ca
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http://front.math.ucdavis.edu/0912.0406
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http://arXiv.org/abs/0912.0406
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