Model Theory with Applications to Algebra and Analysis: Volume 2 VOL.2

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.

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.

The second of a two volume set showcasing current research in model theory and its connections with other areas. With contributions from so many leaders in the field, this book cannot fail to be of interest to model theorists and other mathematicians, from graduate students to senior researchers.

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.