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Preprint Number 475

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475. Isaac Goldbring, Bradd Hart, Thomas Sinclair
Does the theory of tracial von Neumann algebras have a model companion?

Submission date: 1 July 2012.


In this note, we show that, assuming a positive solution to the Connes Embedding Problem (CEP), the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of the hyperfinite II_1 factor does not have quantifier elimination (which is proven without appealing to the CEP).

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Full text arXiv 1207.0169: pdf, ps.

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