A computability-theoretic reformulation of the Connes Embedding Problem
Abstract
The Connes Embedding Problem (CEP) asks whether every separable II1 factor embeds into an ultrapower of the hyperfinite II1 factor. We show that the CEP is equivalent to the computability of the universal theory of every type II1 von Neumann algebra. We also derive some further computability-theoretic consequences of the CEP.
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