APPLICATIONS OF MODEL THEORY TO OPERATOR ALGEBRAS

July 31 -- August 4, 2017
University of Houston
















The masters class will consist of five lectures on the following topics.

  1. Lecture 1: Model theory of metric structures
    2. Introduction to model theory for metric structures, with an emphasis on its applications to C*-algebras.

  2. Lecture 2: Axiomatizability and definability
    3. Axiomatizabile classes of C*-algebras. Definable sets and definable properties.

  3. Lecture 3: Massive C*-algebras
    4. Ultraproducts and central sequence algebras. Algebras with approximately inner flip, strongly self-absorbing C*-algebras, and ultrapowers.

  4. Lecture 4: The effect of the Continuum Hypothesis
    5. The number of nonisomorphic ultrapowers of a C*-algebra. An abstract characterization of the ultrapower of a C*-algebra associated with a nonprincipal ultrafilter.

  5. Lecture 5: Omitting types and model-theoretic forcing
    6. Model theory and the Elliott classification programme. Model-theoretic description of regularity properties of C*-algebras, and applications. Construction of generic C*-algebras.

These lectures will be accessible to graduate students and mathematicians with only a basic background on C*-algebra theory. Open problems and new research opportunities for beginning researchers will also be discussed.