Model Theory of Fields

This book focuses on the fields of real and complex numbers and discusses connections to pure model theory and algebraic geometry. It provides a brief survey of differential Galois theory including Poizat's model theoretic proof of Kolchin's result.

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The model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.