Model Theory with Applications to Algebra and Analysis, Volume 2

✍ Scribed by Zoe Chatzidakis, Dugald Macpherson, Anand Pillay, Alex Wilkie (eds.)

• Publisher: Cambridge University Press
• Year: 2008
• Tongue: English
• Leaves: 444
• Series: London Mathematical Society Lecture Note Series 350
• Edition: 1
• Category: Library

✦ Synopsis

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. This volume completes 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 concluded here reveal 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 two-volume set will undoubtedly appeal to all mathematicians with an interest in model theory and its applications.

✦ Table of Contents

Cover......Page 1
Frontmatter......Page 2
Contents......Page 6
Preface......Page 10
Contributors......Page 14
Conjugacy in groups of finite Morley rank......Page 18
Permutation groups of finite Morley rank......Page 76
A survey of asymptotic classes and measurable structures......Page 142
Counting and dimensions......Page 178
A survey on groups definable in o-minimal structures......Page 194
Decision problems in Algebra and analogues of Hilbert's tenth problem......Page 224
Hilbert's Tenth Problem for function fields of characteristic zero......Page 254
First-order characterization of function field invariants over large fields......Page 272
Nonnegative solvability of linear equations in ordered Abelian groups......Page 290
Model theory for metric structures......Page 332