Logic Seminar
John Baldwin
UIC
The unreasonable effectiveness of model theory in analysis
Abstract: We attempt to delineate the characteristics of model theory that
account for its impact across mathematics. The {\em formalization}
of {\em specific} areas of mathematics is the basic theme; this
allows axiomatizations that respect the methodologies of each area.
Secondly, classification theory allows the recognition of common
methodologies in widely distinct areas. We distinguish two ways in
which model theory provides tools to `tame' analysis via first order logic:
{\em Axiomatic Analysis} and {\em Definable Analysis}.
In this talk we focus on
Axiomatic Analysis and specifically in the use of the model theory of
differentially closed fields to address century old problems around the
transcendence of solutions of to Painlev{\'e} equations. Thus we give
some context for recent papers of Pillay, Nagloo, and Freitag.
Tuesday November 21, 2017 at 4:00 PM in SEO 427