Devrim Pekmezci : Randomizations of First-Order Structures

Posted by Ryan Carpenter , part of the Louise Hay Logic Seminar.

At

Feb. 25, 2026, 3 p.m.

In

512 SEO

Abstract

The notion of randomization was introduced by H. Jerome Keisler and later refined by Itaï Ben Yaacov and Keisler within the framework of continuous model theory. A randomization of a first-order structure M is a continuous structure with two sorts: one for random elements of M, and one for events in an underlying probability space. All randomizations of a fixed structure M are models of the same complete continuous theory, which admits a natural axiomatization and quantifier elimination. In this talk, we shall briefly review some background on continuous model theory and the model theory of atomless probability spaces, then define the randomization of a first-order structure, present its axiomatization, and conclude with examples and properties of randomization.