Model Theory with Applications to Algebra and Analysis Volume 1 [Paperback]

Account of current research in model theory and its connections with algebra and analysis; contributions from leaders in the field.The first 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.The first 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.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.Preface; List of contributors; 1. Model theory and stability theory, with applications in differential algebra and algebraic geometry Anand Pillay; 2. Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations Anand Pillay; 3. Schanuel's conjecture for non-isoconstanlƒ