Model Theory, Algebra, and Geometry

Model Theory, Algebra, and Geometry

Author: Professor of Mathematics Anand Pillay

Publisher: Cambridge University Press

ISBN: 0521780683

Category: Mathematics

Page: 227

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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, Algebra, and Geometry
Language: en
Pages: 227
Authors: Professor of Mathematics Anand Pillay
Categories: Mathematics
Type: BOOK - Published: 2000-07-03 - Publisher: Cambridge University Press

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
Model Theory and Algebraic Geometry
Language: en
Pages: 211
Authors: Elisabeth Bouscaren
Categories: Mathematics
Type: BOOK - Published: 1998 - Publisher: Springer Science & Business Media

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1
Language: en
Pages: 346
Authors: Raf Cluckers, Johannes Nicaise, Julien Sebag
Categories: Mathematics
Type: BOOK - Published: 2011-09-22 - Publisher: Cambridge University Press

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time,
A Guide to Classical and Modern Model Theory
Language: en
Pages: 371
Authors: Annalisa Marcja, Carlo Toffalori
Categories: Philosophy
Type: BOOK - Published: 2012-09-10 - Publisher: Springer Science & Business Media

This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for
Model Theory in Algebra, Analysis and Arithmetic
Language: en
Pages: 195
Authors: Lou van den Dries, Jochen Koenigsmann, H. Dugald Macpherson, Anand Pillay, Carlo Toffalori, Alex J. Wilkie
Categories: Mathematics
Type: BOOK - Published: 2014-09-20 - Publisher: Springer

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the