Submission date: 1 July 2012.

Abstract:

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).

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1207.0169: pdf, ps.