Model Theory, Algebra, and Geometry (Paperback)

Deirdre Haskell

ISBN 10: 0521143497 / ISBN 13: 9780521143493

Published by Cambridge University Press, Cambridge, 2010

About this Item

Paperback. Model theory has 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 (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, 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 (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields. Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. In this book, originally published in 2000, leading experts provide the necessary background to understanding the model theory and mathematics behind these applications. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521143493

Bibliographic Details

• Title: Model Theory, Algebra, and Geometry (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2010
• Language: English
• ISBN 10: 0521143497
• ISBN 13: 9780521143493
• Binding: Paperback
• Condition: new

About this title

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).

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.