The Theory of Tracial Von Neumann Algebras Does Not Have A Model Companion
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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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