Model theory and the QWEP conjecture

TL;DR

This paper explores the model-theoretic equivalence of Kirchberg's QWEP conjecture with the elementary equivalence of certain C*-algebras, providing new insights into their logical properties.

Contribution

It establishes the equivalence between the QWEP conjecture and elementary equivalence of specific C*-algebras, offering a novel model-theoretic perspective.

Findings

QWEP conjecture is equivalent to $C^*(\mathbb{F})$ being elementarily equivalent to a QWEP C*-algebra

Provides model-theoretic remarks on WEP and LLP C*-algebras

Links between algebraic properties and logical equivalences in operator algebras

Abstract

We observe that Kirchberg's QWEP conjecture is equivalent to the statement that $C^*(\mathbb{F})$ is elementarily equivalent to a QWEP C$^*$ algebra. We also make a few other model-theoretic remarks about WEP and LLP C$^*$ algebras.