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Preprint Number 2185

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2185. Jananan Arulseelan, Isaac Goldbring, and Bradd Hart
The undecidability of having the QWEP

Submission date: 14 May 2022


We show that neither the class of C*-algebras with Kirchberg's QWEP property nor the class of W*-probability spaces with the QWEP property are effectively axiomatizable (in the appropriate languages). The latter result follows from a more general result, namely that the hyperfinite III_1 factor does not have a computable universal theory in the language of W*-probability spaces. We also prove that the Powers' factors R_λ, for 0<λ<1, when equipped with their canonical Powers' states, do not have computable universal theory.

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Full text arXiv 2205.07102: pdf, ps.

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