THE UNIVERSAL THEORY OF THE HYPERFINITE II $_1$ FACTOR IS NOT COMPUTABLE
Isaac Goldbring, Bradd Hart · Bulletin of Symbolic Logic · 2024
Abstract We show that the universal theory of the hyperfinite II $_1$ factor is not computable. The proof uses the recent result that MIP*=RE. Combined with an earlier observation of the authors, this yields a proof that the Connes Embedding Problem has a negative solution that avoids the equivalences with Kirchberg’s QWEP Conjecture and Tsirelson’s Problem.