The undecidability of having the QWEP
Jananan Arulseelan, Isaac Goldbring, Bradd Hart · arXiv (Cornell University) · 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 $\mathcal{R}_λ$, for $0<λ<1$, when equipped with their canonical Powers' states, do not have computable universal theory.