Journal of Symbolic Logic

The theory of tracial von Neumann algebras does not have a model companion

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.

Article information

Source
J. Symbolic Logic Volume 78, Issue 3 (2013), 1000-1004.

Dates
First available in Project Euclid: 6 January 2014

https://projecteuclid.org/euclid.jsl/1389032287

Digital Object Identifier
doi:10.2178/jsl.7803170

Mathematical Reviews number (MathSciNet)
MR3135510

Zentralblatt MATH identifier
1316.03019

Citation

Goldbring, Isaac; Hart, Bradd; Sinclair, Thomas. The theory of tracial von Neumann algebras does not have a model companion. J. Symbolic Logic 78 (2013), no. 3, 1000--1004. doi:10.2178/jsl.7803170. https://projecteuclid.org/euclid.jsl/1389032287