BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Artem Chernikov (UCLA) DTSTART:20201008T180000Z DTEND:20201008T190000Z DTSTAMP:20260423T035729Z UID:OLS/38 DESCRIPTION:Title: Ide mpotent Keisler measures\nby Artem Chernikov (UCLA) as part of Online logic seminar\n\n\nAbstract\nIn model theory\, a type is an ultrafilter on the Boolean algebra of definable sets\, and is the same thing as a finite ly additive {0\,1}-valued measure. This is a special kind of a Keisler mea sure\, which is just a finitely additive real-valued probability measure o n the Boolean algebra of definable sets. If the structure we are consideri ng expands a group (i.e. the group operations are definable)\, it often li fts to a natural semigroup operation on the space of its types/measures\, and it makes sense to talk about the idempotent ones among them. For insta nce\, idempotent ultrafilters on the integers provide an elegant proof of Hindman's theorem\, and fit into this setting taking the structure to be ( Z\,+) with all of its subsets named by predicates. On the other hand\, in the context of locally compact abelian groups\, classical work by Wendel\, Rudin\, Cohen (before inventing forcing) and others classifies idempotent Borel measures\, showing that they are precisely the Haar measures of com pact subgroups. I will discuss recent joint work with Kyle Gannon aiming t o unify these two settings\, leading in particular to a classification of idempotent Keisler measures in stable theories.\n LOCATION:https://researchseminars.org/talk/OLS/38/ END:VEVENT END:VCALENDAR