Model Theory with Applications to Algebra and Analysis

The first of a two-volume set showcasing the current research in model theory and its connections with number theory algebraic geometry real analytic geometry and differential algebra. This volume begins with 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 included showcase 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 noncommutative 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.