Model Theory and Geometry

Abstract

This thesis gives a self-contained exposition of Peterzil and Starchenko's o-minimal reproof of Chow's Theorem, assuming no model theoretic prerequisites. Intended for beginners, I start from the necessary model-theoretic foundations, such as compactness and quantifier elimination for algebraically closed and real closed fields. I then develop the basic theory of o-minimal structures, with particular emphasis on cell decomposition, definable topology, and the theory of curves. These tools are brought together in Peterzil and Starchenko's integral-free theory of o-minimal complex analysis, which implies a proof of Chow's theorem.