Computable Continuous Logic, QWEP, and Type III Factors

Jananan Arulseelan, McMaster University

By the recent MIP*=RE result, the QWEP conjecture is known to be false. Consequently, the universal theory of the hyperfinite II_1 factor is not computable. We will explain these results and their context and then discuss the uncomputability of the universal theories of other Powers factors and the lack of an effective axiomatization of QWEP C^∗ algebras. As an application we show that there is a ultraproduct of non-QWEP algebras with QWEP. This is joint work with Isaac Goldbring and Bradd Hart. 

MC 5479