Chatzidakis Z.M., Macpherson D., Pillay A., Wilkie A. (Eds.) Model theory with applications to algebra and analysis. Volume 2

Cambridge University Press, 2008. — 444 p. — (London Mathematical Society Lecture Note volume 350). — ISBN 13 9780521709088.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.Conjugacy in groups of finite Morley rank
Permutation groups of finite Morley rank
A survey of asymptotic classes and measurable structures
Counting and dimensions
A survey on groups definable in o-minimal structures
Decision problems in Algebra and analogues of Hilbert’s tenth problem
Hilbert’s Tenth Problem for function fields of characteristic zero
First-order characterization of function field invariants over large fields
Nonnegative solvability of linear equations in ordered Abelian groups
Model theory for metric structures