The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one
leads to several applications: we answer affirmatively, for the class of stable rank-one C …

Let A be a separable, unital, simple, Z-stable, nuclear C⁎-algebra, and let α: G→ Aut (A) be
an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G …

This book is shorter than In Search of Lost Time, is easier to read than Principia
Mathematica, and has more mathematical content than War and Peace. 1, 2 It provides an …

The Connes embedding problem (CEP) is a problem in the theory of tracial von Neumann
algebras and asks whether or not every tracial von Neumann algebra embeds into an …

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 …

Using Cuntz semigroup techniques, we characterize when limit traces are dense in the
space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density …

We study sufficient conditions under which a nowhere scattered $\mathrm {C}^* $-algebra $
A $ has a nowhere scattered multiplier algebra $\mathcal {M}(A) $, that is, we study when …

Abstract Kirchberg's Embedding Problem (KEP) asks whether every separable C⁎ algebra
embeds into an ultrapower of the Cuntz algebra O 2. In this paper, we use model theory to …

The findings reported in this paper aim to garner the interest of both model theorists and
operator algebraists alike. Using a novel blend of model theoretic and operator algebraic …

We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence,
the category admits products and ultraproducts. We further show that the scaled Cuntz …