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arXiv · 2205.07102

The undecidability of having the QWEP

Jananan Arulseelan·Isaac Goldbring·Bradd Hart
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Abstract

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 $\mathcal{R}_\lambda$, for $0<\lambda<1$, when equipped with their canonical Powers' states, do not have computable universal theory.

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Jananan Arulseelan, Isaac Goldbring, Bradd Hart. 2022-05-14. The undecidability of having the QWEP. https://arxiv.org/abs/2205.07102

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