Model Theory, Algebra, and Geometry (Mathematical Sciences Research Institute Publications, Series Number 39) - Hardcover

Hardcover

ISBN 10: 0521780683 ISBN 13: 9780521780681

Publisher: Cambridge University Press, 2000

Synopsis

Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. It provides a unifying framework for the understanding of old results and more recently has led to significant new results, such as a proof of the Mordell-Lang conjecture for function fields in positive characteristic. Perhaps surprisingly, it is sometimes the most abstract aspects of model theory that are relevant to those applications. This book gives the necessary background for understanding both the model theory and the mathematics behind the applications. Aimed at graduate students and researchers, it contains introductory surveys by leading experts covering the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations), and introducing and discussing the diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) to which the model theory is applied. The book begins with an introduction to model theory by David Marker. It then broadens into three components: pure model theory (Bradd Hart, Dugald Macpherson), geometry(Barry Mazur, Ed Bierstone and Pierre Milman, Jan Denef), and the model theory of fields (Marker, Lou van den Dries, Zoe Chatzidakis).

About this title

Book Description

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2000
• ISBN 10: 0521780683
• ISBN 13: 9780521780681
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 236
• Editor: Haskell Deirdre, Pillay Anand, Steinhorn Charles