We recommend that non-UIC participants attend online. Any non-UIC participants who would like to attend in-person events need to register with the organizer at least three days before the seminar. If you have any questions, please contact Eloy Reyes.

Logic Seminar

Artem Chernikov
UCLA
Keisler randomization and higher order VC-dimension
Abstract: A randomization of a first-order structure M, introduced by Keisler, is a structure M^R in continuous logic whose elements are the "random" elements of M. One can think of it as a continuous structure whose types correspond to probability measures on the space of types of the original structure. Randomization preserves certain model-theoretic tameness properties, e.g. stability and NIP. The latter was demonstrated by Ben Yaacov via developing aspects of the VC-theory (Vapnik-Chervonenkis) in the continuous setting, connected to earlier work of Talagrand and others. A more general hierarchy of n-dependent theories was introduced by Shelah, with the case n=1 corresponding to NIP: a theory is n-dependent if the edge relation of an infinite generic (n+1)-hypergraph is not definable. We will discuss n-dependence in continuous logic and demonstrate that n-dependence is also preserved by Keisler randomization: the main point is that the average of a family of uniformly n-dependent functions is n-dependent. Our proof relies on structural Ramsey theory and multidimensional de Finetti-type results (and provides in particular a new proof in the NIP case). Joint work with Henry Towsner.
Tuesday March 29, 2022 at 4:00 PM in 636 SEO
Web Privacy Notice HTML 5 CSS FAE
UIC LAS MSCS > persisting_utilities > seminars >