John T. Baldwin : DIFFERENTIALLY CLOSED FIELDS AND $L_{\omega_1,\omega}$-CATEGORICITY OF UNIVERSAL COVERS

Posted by Tom Benhamou , part of the Logic Seminar.

At

Jan. 24, 2023, 4 p.m.

In

636 SEO

Abstract

Sacks’ student Lenore Blum provided the first intuitive axiomatization of the theory of differentially closed fields. Moreover, she established the $\omega$-stability of the theory and thus the uniqueness of the prime model. Sacks book, Saturated Model Theory, was the first book expounding stability theory and presented the notion of a differentially closed field to a general logical audience. Zilber initiated the program of proving $L_{\omega_1,\omega}$-categoricity in power for ‘canonical mathematical structures’. In this talk we will describe recent advances unifying these two programs.