Synopsis
The model theory of fields is an area for important interactions between mathematical, logical and classical mathematics. Recently, there have been major applications of model theoretic ideas to real analytic geometry and diophantine geometry. This book provides an introduction to this fascinating subject. In addition to introducing the basic model theory of the fields of real and complex numbers, we concentrate on differential fields and separably closed fields, the two theories used in Hrushovski's proof of the Mordell-Lang conjecture for function fields. This book is of interest to graduate students in either logic or in related areas of mathematics such as differential algebra or real algebraic geometry.
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Book Description
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.
About the Author
Dave Marker is professor at the University of Chicago. His research includes model theory and its applications to real algebraic and analytic geometry, exponentiation, and differential algebra.Margit Messmer is a professor at the University of Illinois, Urbana-Champaign. Her research interest include mathematical logic and model theory.Anand Pillay is a professor at the University of Illinois, Urbana-Champaign. His research interests include model theory and applications to algebra, geometry, and number theory.
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