Model Theory with Applications to Algebra and Analysis

doi:10.1017/CBO9780511735219

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.

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Model Theory with Applications to Algebra and Analysis

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xii

Contributors
pp xiii-xvi

Conjugacy in groups of finite Morley rank
pp 1-58

Permutation groups of finite Morley rank
pp 59-124

A survey of asymptotic classes and measurable structures
pp 125-160

Counting and dimensions
pp 161-176

A survey on groups definable in o-minimal structures
pp 177-206

Decision problems in Algebra and analogues of Hilbert's tenth problem
pp 207-236

Hilbert's Tenth Problem for function fields of characteristic zero
pp 237-254

First-order characterization of function field invariants over large fields
pp 255-272

Nonnegative solvability of linear equations in ordered Abelian groups
pp 273-314

Model theory for metric structures
pp 315-427

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Model Theory with Applications to Algebra and Analysis

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