Monday, June 18, 2012, 16.15

Room 1.007, Mathematisches Institut, Universität Bonn

Speaker: Meeri Kesälä (University of Helsinki)

Title: Introduction to non-elementary model theory and applications

Abstract:

Classically model theory studies classes of infinite structures, which are the models of a theory in first order logic. These are called elementary classes. Powerful machinery, such as the tools from geometric stability theory, have been developed to analyze elementary classes. Furthermore, the tools have been applied to solve questions from many fields of mathematics, for example algebraic geometry and number theory.

In this talk we give some motivation and examples why and how this machinery has been generalized beyond first-order definable classes, to so called non-elementary classes. We focus on examples by Zilber and Kirby motivated by the study of the field of complex numbers with the exponent function.

If time is left, we discuss some connections of non-elementary model theory to set-theoretical combinatorics. No prequisities in model theory are needed for the talk.