## Model theory: Your new favourite area of maths

Warwick Mathematics and Philosophy, 17th March 2016

Abstract:

Model theory is a thriving area of mathematics with appeal to mathematicians and philosophers alike. In this talk I will act as a salesman for model theory, doing my best to convince the audience of both its utility and its beauty. I will attempt to mix some practical, hands-on technical aspects of the subject with its more philosophical features. I will start with some history and then move on to a key notion of model theory, namely that of a type. I will then go over the very useful technique of quantifier elimination before discussing some of model theory's great (and ongoing) successes, for example nonstandard analysis, Hrushovski's proof of the Manin–Mumford conjecture, and neo-stability. I will remark on philosophical implications throughout the talk. Note that I will assume knowledge of first-order logic, such as the compactness and Löwenheim–Skolem theorems.

Model theory is a thriving area of mathematics with appeal to mathematicians and philosophers alike. In this talk I will act as a salesman for model theory, doing my best to convince the audience of both its utility and its beauty. I will attempt to mix some practical, hands-on technical aspects of the subject with its more philosophical features. I will start with some history and then move on to a key notion of model theory, namely that of a type. I will then go over the very useful technique of quantifier elimination before discussing some of model theory's great (and ongoing) successes, for example nonstandard analysis, Hrushovski's proof of the Manin–Mumford conjecture, and neo-stability. I will remark on philosophical implications throughout the talk. Note that I will assume knowledge of first-order logic, such as the compactness and Löwenheim–Skolem theorems.