On regular ultrafilters, Boolean ultrapowers, and Keisler's order

In this paper we analyse and compare two different notions of regularity for filters on complete Boolean algebras. We also announce two results from a forthcoming paper in preparation, which provide a characterization of Keisler's order in terms of Boolean ultrapowers

Generically Stable Measures and Distal Regularity in Continuous Logic

We develop a theory of generically stable and smooth Keisler measures in NIP metric theories, generalizing the case of classical logic. Using smooth extensions, we verify that fundamental properties of (Borel)-definable measures and the Morley product hold in the NIP metric setting. With these results, we prove that as in discrete logic, generic stability can be defined equivalently through definability properties, statistical properties, or behavior under the Morley product. We also examine weakly orthogonal Keisler measures, characterizing weak orthogonality in terms of various analytic regularity properties. We then examine Keisler measures in distal metric theories, proving that as in discrete logic, distality is characterized by all generically stable measures being smooth, or by all pairs of generically stable measures being weakly orthogonal. We then use this, together with our results on weak orthogonality and a cutting lemma, to find analytic versions of distal regularity and the strong Erd\H{o}s-Hajnal property

Model Theory: Around Valued Fields and Dependent Theories

The general topic of the meeting was “Valued fields and related structures”. It included both applications of model theory, as well as so-called “pure” model theory: the classification of first order structures using new techniques extending those developed in stable theories