Synopses & Reviews
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Synopsis
Model theory (a branch of mathematical logic) has, in recent years, made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. This book, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory is covered and diverse areas of geometry are also introduced and discussed, all by leading experts in their fields.
Table of Contents
1. Introduction to model theory David Marker; 2. Some classical model theory of fields Lou van den Dries; 3. Introduction to the model theory of differential fields David Marker; 4. Notes on o-minimality and variations Dugald Macpherson; 5. A survey on the model theory of difference fields Zoe Chatzidakis; 6. Dimension theory Bradd Hart; 7. Model theory and the Mordell-Lang conjecture Barry Mazur; 8. Semialgebraic and subanalytic geometry Edward Bierstone; 9. Model theory and geometry Jan Denef.