Ryan Carpenter : On O-Minimally Definable Groups and Fields

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

At

Jan. 27, 2025, 3 p.m.

In

612 SEO

Abstract

In his 1988 paper "On Groups and Fields Definable in o-Minimal Structures", Anand Pillay gives a characterization of groups definable in o-minimal structures by which they look like manifolds over the underlying o-minimal structure. He notes that the argument runs virtually unchanged for o-minimally definable fields, and he uses this to deduce that all o-minimally definable fields are either real or algebraically closed. In this talk, I will present the relevant background material on o-minimality as well as these three key results which highlight a way by which we may consider o-minimal structures as nice.