Title: Ultrapowers, asymptotic sequences, and classification
Speaker: Ilijas Farah (York University)
Abstract: Ultrapowers were discovered, apparently independently, by operator algebraists and logicians (in that order!) in the1950s. Since the early 1970s, the ultrapowers of separable operator algebras associated with nonprincipal ultrafilters on N have been one of the main tools in classification of von Neumann algebras and, more recently, C*-algebras. As all properties of such ultrapowers can be explained by two of their abstract properties, countable saturation and Los’s theorem, it was to be expected that logic may play a role in the theory. I’ll survey some of the progress in the past ten years and present some more recent results about the relation between the ultrapowers and asymptotic sequence algebras. (The latter are known to logicians as the reduced products associated with the Frechet ideal.)
