We survey the developments in the model theory of tracial von Neumann algebras that have
taken place in the last 15 years. We discuss the appropriate first-order language for …

We present an introduction to modern continuous model theory with an emphasis on its
interactions with topics covered in this volume such as C∗-algebras and von Neumann …

Recall that a unitary in a tracial von Neumann algebra is Haar if τ (un)= 0 for all n∈ N. We
introduce and study a new Borel equivalence relation∼ N on the set of Haar unitaries in a …

The notion of a∗-law or∗-distribution in free probability is also known as the quantifier-free
type in Farah, Hart, and Sherman's model-theoretic framework for tracial von Neumann …

We introduce and study the family of uniformly super McDuff II 1 factors. This family is shown
to be closed under elementary equivalence and also coincides with the family of II 1 factors …

Asymptotic freeness in tracial ultraproducts Page 1 Forum of Mathematics, Sigma (2024), Vol.
12:e88 1–22 doi:10.1017/fms.2024.93 RESEARCH ARTICLE Asymptotic freeness in tracial …

In this paper we study multi-matrix models whose potentials are small perturbations of the
quadratic potential associated with independent GUE random matrices. More precisely, we …

In this paper we show various new structural properties of free group factors using the recent
resolution (due independently to Belinschi-Capitaine and Bordenave-Collins) of the …

We prove an analog of the disintegration theorem for tracial von Neumann algebras in the
setting of elementary equivalence rather than isomorphism, showing that elementary …

We investigate the problem of elementary equivalence of the free group factors, that is, do all
free group factors $ L (\mathbb {F} _n) $ share a common first-order theory? We establish a …