Model theory with applications to algebra and analysis. Volume 2 / [edited by] Zoé Chatzidakis [and three others].

Format:

Book

Contributor:

Chatzidakis, Zoé Maria, editor.

Series:

London Mathematical Society lecture note series ; 350.

London Mathematical Society lecture note series ; 350

Language:

English

Subjects (All):

Model theory.

Physical Description:

1 online resource (xv, 427 pages) : digital, PDF file(s).

Other Title:

Model Theory with Applications to Algebra & Analysis

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

The second of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and non-commutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this book will undoubtedly appeal to all mathematicians with an interest in model theory and its applications, from graduate students to senior researchers and from beginners to experts.

Contents:

1.5 Generic n-Transitivity Revisited2 Bounds on rank; 2.1 Examples; 2.2 Reduction to generic multiple transitivity; 3 The definable socle; 3.1 The main case division; 3.2 The torsion-free divisible case; 3.3 Simple socles; 3.4 Elementary abelian socles; 3.5 Nonabelian socles; 4 Actions of finite groups on connected solvable groups; 4.1 Generalities; 4.2 Actions of symmetric groups; 4.3 Groups covering Sym(n); 5 Simple permutation groups; 5.1 The four types; 5.2 Even type groups; 5.3 Odd type groups; 5.4 Primitive simple groups of odd type; 5.5 Tying up the loose ends

6 Generic multiple transitivity6.1 An extremal case; 6.2 The affine case; 6.3 The point stabilizer; 6.4 Small affine groups; 6.5 An inductive step for Problem 13; 6.6 The Curtis-Tits Theorem; 6.7 Pseudoreflection groups; 6.8 One more problem; 7 Problem list; References; A survey of asymptotic classes and measurable structures; 1 Introduction; 2 Asymptotic classes; 3 Measurable structures; 4 Smoothly approximable structures; 5 Measure and difference fields; 6 Asymptotic classes of simple groups; 7 Groups of low dimension; 8 Further questions; References; Counting and dimensions; Summary

Introduction

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

"The volumes grew out of the semester on 'Model Theory and Applications to Algebra and Analysis' which took place at the Isaac Newton Institute (INI), Cambridge, from January to July 2005"--Preface.

Includes bibliographical references.

ISBN:

1-139-88272-4

1-107-36791-3

1-107-37245-3

1-107-36300-4

1-107-36831-6

1-299-40551-7

1-107-36545-7

0-511-73521-9

OCLC:

843204405