Combinatorial Set Theory of C*-Algebras

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The author is at the forefront of research on the interplay between logic and operator algebras (C*-algebras, in particular). The deep level of scholarship contained in these pages opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make this book a convenient, self-contained source for students. Exercises form an integral part of the text. They widen and deepen the material from the corresponding chapters. Other exercises serve as a warmup for the latter chapters.

This second edition furthers the aims of the first, improving proofs and providing new insights into the relationship between logic and operator algebras. It has been expanded, adding new lemmas, definitions, propositions, and exercises. The book provides a comprehensive analysis of ultraproducts of tracial von Neumann algebras. It also introduces Kirchberg’s epsilon-test for ultraproducts and reduced products, along with its strict strengthening.