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arXiv · 1207.0169

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

Isaac Goldbring·Bradd Hart·Thomas Sinclair
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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. 2012-07-26. The theory of tracial von Neumann algebras does not have a model companion. https://arxiv.org/abs/1207.0169

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