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

  • Isaac Goldbring (a1), Bradd Hart (a2) and Thomas Sinclair (a3)


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 II1 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 II1 factors.



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