Hongyu Zhu : The Borel complexity of the class of models of first-order theories

Posted by Matthew Harrison-Trainor , part of the Logic Seminar.

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Oct. 22, 2024, 4 p.m.

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636 SEO

Abstract

Viewed as a subset of Cantor space, the class of countable models Mod(T) of any first order theory T is always Borel. A natural question, then, is the relationship between its descriptive complexity and the complexity of the underlying theory. Using theorems of López-Escobar and Solovay, we give a more precise characterization of the complexity of Mod(T) in terms of that of T. We also discuss some applications to models of PA and infinitary logic. (This is based on joint work with Andrews, Gonzalez, Lempp, Rossegger, and related to recent work of Enayat and Visser.)