Model Theory, Algebra, and Geometry [Paperback]

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.Model theory (a branch of mathematical logic) has, in recent years, made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases it is the most abstract aspects of model theory which are relevant. 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.Model theory (a branch of mathematical logic) has, in recent years, made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases it is the most abstract aspects of model theory which are relevant. 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.Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. It provides a unifying flÓ{