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15 August 2017 II1 factors with nonisomorphic ultrapowers
Rémi Boutonnet, Ionuţ Chifan, Adrian Ioana
Duke Math. J. 166(11): 2023-2051 (15 August 2017). DOI: 10.1215/00127094-0000017X

Abstract

We prove that there exist uncountably many separable II1 factors whose ultrapowers (with respect to arbitrary ultrafilters) are nonisomorphic. In fact, we prove that the families of nonisomorphic II1 factors originally introduced by McDuff are such examples. This entails the existence of a continuum of nonelementarily equivalent II1 factors, thus settling a well-known open problem in the continuous model theory of operator algebras.

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Rémi Boutonnet. Ionuţ Chifan. Adrian Ioana. "II1 factors with nonisomorphic ultrapowers." Duke Math. J. 166 (11) 2023 - 2051, 15 August 2017. https://doi.org/10.1215/00127094-0000017X

Information

Received: 29 July 2016; Revised: 16 November 2016; Published: 15 August 2017
First available in Project Euclid: 28 March 2017

zbMATH: 1384.46040
MathSciNet: MR3694564
Digital Object Identifier: 10.1215/00127094-0000017X

Subjects:
Primary: 46L10
Secondary: 03C20

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 11 • 15 August 2017
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