A computability-theoretic reformulation of the Connes Embedding Problem

Abstract

The Connes Embedding Problem (CEP) asks whether every separable II_1 factor embeds into an ultrapower of the hyperfinite II_1 factor. We show that the CEP is equivalent to the computability of the universal theory of every type II_1 von Neumann algebra. We also derive some further computability-theoretic consequences of the CEP.

9 pages

References in corpus (1)

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

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