Feb 4 2025

Logic Seminar: Model Theoretic Events, by Kyle Gannon

February 4, 2025

3:30 PM - 4:20 PM

Location

636 SEO

Address

Chicago, IL

Calendar

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Kyle Gannon (Peking University): Model Theoretic Events

This talk is motivated by the following two soft questions: How do we sample an
infinite sequence from a first order structure? What model theoretic properties might hold on
almost all sampled sequences? We advance a plausible framework in an attempt to answer these
kinds of questions. The central object of this talk is a probability space. The underlying set of
our space is a standard model theoretic object, namely the space of types in countably many
variables over a monster model. Our probability measure is an iterated Morley product of a
fixed Borel-definable Keisler measure. Choosing a point randomly in this space with respect to
our distribution yields a random generic type in infinitely many variables. We are interested in
which model theoretic events hold for almost all random generic types. Two different kinds of
events will be discussed: (1) The event that the induced structure on a random generic type is
isomorphic to a fixed structure; (2) the event that a random generic type witnesses a dividing
line.

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