Model Theory with Applications to Algebra and Analysis: Volume 2

by Zoé Chatzidakis, Dugald Macpherson, Anand Pillay, Alex Wilkie

Overview

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.

Product Details

ISBN-13:	9780521709088
Publisher:	Cambridge University Press
Publication date:	05/22/2008
Series:	London Mathematical Society Lecture Note Series , #350
Pages:	444
Product dimensions:	6.00(w) x 8.90(h) x 1.00(d)

About the Author

Zoé Chatzidakis is Directeur de recherches in the Centre National de la Recherche Scientifique (CNRS) at the Université de Paris VII.

Dugald Macpherson is a Professor in the School of Mathematics at the University of Leeds.

Anand Pillay is a Professor in the School of Mathematics at the University of Leeds and Swanlund Chair Emeritus in the Mathematics Department at the University of Illinois.

Alex Wilkie is Fielden Professor of Pure Mathematics at the University of Manchester.

Table of Contents

Preface; List of contributors; 1. Conjugacy in groups of finite Morley rank Olivier Frécon and Eric Jaligot; 2. Permutation groups of finite Morley rank Alexandre Borovik and Gregory Cherlin; 3. A survey of asymptotic classes and measurable structures Richard Elwes and Dugald Macpherson; 4. Counting and dimensions Ehud Hrushovski and Frank Wagner; 5. A survey on groups definable in o-minimal structures Margarita Otero; 6. Decision problems in algebra and analogues of Hilbert's tenth problem Thanases Pheidas and Karim Zahidi; 7. Hilbert's tenth problem for function fields of characteristic zero Kirsten Eisenträger; 8. First-order characterization of function field invariants over large fields Bjorn Poonen and Florian Pop; 9. Nonnegative solvability of linear equations in ordered Abelian groups Philip Scowcroft; 10. Model theory for metric structures IItaï Ben Yaacov, Alexander Berenstein, C. Ward Henson and Alexander Usvyatsov.