Submission date: 14 May 2022

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 R_λ, for 0<λ<1, when equipped with their canonical Powers' states, do not have computable universal theory.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2205.07102: pdf, ps.