Title: New Directions in the Computable Model Theory of von Neumann Algebras
Abstract: The majority of work in the model theory of von Neumann algebras to date has been done entirely in the tracial setting. This is, in part, due to the lack of a user-friendly axiomatization that includes non-tracial von Neumann algebras. After a quick review of the prerequisite material, we will discuss computable axiomatizations and their utility. We will sample some of the key theoretical hurdles to a working computable model theory of non-tracial von Neumann algebras and how they were overcome. We will then consider some directions for future work. Joint work with Isaac Goldbring, Bradd Hart, and Thomas Sinclair.
