11:00
This talk focuses on the logic side of the following result: the non-definability of free independence in the theory of tracial von Neumann algebras and C*-probability spaces. I will introduce continuous model theory, which is suitable for the study of metric structures. Definability in the continuous setting differs slightly from that in the discrete case. I will introduce its definition, give examples of definable sets, and prove an equivalent ultrapower condition of it. A. Berenstein and C. W. Henson exposited model theory for probability spaces in 2023, which was done with continuous model theory. It makes it natural for us to consider the definability of the notion of free independence in probability spaces. I will explain our result, which gives an example of a non-definable set.
This is work with William Boulanger and Emma Harvey, supervised by Jenny Pi and Jakub Curda.