Logic Seminar
Henry Towsner
University of Pennsylvania
Relatively Random First-Order Structures
Abstract: The Aldous-Hoover Theorem gives a characterization of those random processes which generate "exchangeable" first-order structures. A random first-order structure on the natural numbers is exchangeable if, after any permutation of the natural numbers, it has the same distribution. Although combinatorial proofs now exist, the original proof was model-theoretic: one views as exchangeable process as one given by sampling countably many points from an ultraproduct according to its Loeb measure.
For some purposes, full exchangeability is too strong. We investigate "relative exchangeability", where we only require that the distribution be preserved by automorphisms of a fixed first-order structure M. Depending on the amalgamation properties of the finite substructures of M, we obtain various generalizations of the Aldous-Hoover Theorem to this setting.
Tuesday March 8, 2016 at 4:00 PM in SEO 427