Model Theory of Fields [Hardcover]

This book introduces the active area of the model theory of fields, concentrating on connections to stability theory.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 MordellLang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.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 MordellLang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fifth publication in the Lecture Notes in Logic series, the authors give an insightful introduction to the fascinating subject of the model theory of fields, concentrating on its connections to stability theory. In the first two chapters David Marker gives an overview of the model theory of algebraically closed, real closed and differential fields. In the third chapter Anand Pillay gives a proof that there are 2? non-isomorphic countable differential closed fields. Finally, Margit Messmer gives a survey of the model theory of separably closed fields of characteristic p >0.Preface; 1. Introduction to the model theory of fields David Marker; 2. Model theory of differential fields David Marker; 3. Differential algebraic groups and the number of countable differentially closed fields Anand Pillay; 4. Some model theory of separably closed fields Margit Messmer; Index.