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September 2013 The theory of tracial von Neumann algebras does not have a model companion
Isaac Goldbring, Bradd Hart, Thomas Sinclair
J. Symbolic Logic 78(3): 1000-1004 (September 2013). DOI: 10.2178/jsl.7803170

Abstract

In this note, we show that the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of any locally universal, McDuff II$_1$ factor does not have quantifier elimination. We also show how a positive solution to the Connes Embedding Problem implies that there can be no model-complete theory of II$_1$ factors.

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Isaac Goldbring. Bradd Hart. Thomas Sinclair. "The theory of tracial von Neumann algebras does not have a model companion." J. Symbolic Logic 78 (3) 1000 - 1004, September 2013. https://doi.org/10.2178/jsl.7803170

Information

Published: September 2013
First available in Project Euclid: 6 January 2014

zbMATH: 1316.03019
MathSciNet: MR3135510
Digital Object Identifier: 10.2178/jsl.7803170

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 3 • September 2013
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