Model theory with applications to algebra and analysis

The first of a two volume set showcasing current research in model theory andits connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essaysand 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 aroundMordell-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 fromso 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. Includes significant new results from leading researchers in model theory and related areas. All major recent developments in the area are discussed; future directions in the area are proposed. Essential reading for all model theorists and any student or researcher interested in the topic INDICE: 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-isoconstant elliptic curves over function fields Daniel Bertrand; 4. An afterthought on the generalized Mordell-Lang conjecture Damian Rössler; 5. On the definitions of Difference Galois Groups Zoé Chatzidakis, Charlotte Hardouin and Michael F. Singer; 6. Differentially valued fields are not differentially closed Thomas Scanlon; 7. Complex analytic geometry in a nonstandard setting Ya'acov Peterzil and Sergei Starchenko; 8. Model theory and Kähler geometry Rahim Moosa and Anand Pillay; 9. Some local definability theory for holomorphic functions A. J. Wilkie; 10. Some observations about the real andimaginary parts of complex Pfaffian functions Angus Macintyre; 11. Fusion of structures of finite Morley rank Martin Ziegler; 12.Establishing the o-minimality for expansions of the real field Jean-Philippe Rolin; 13. On the tomography theorem by P. Schapira Sergei Starchenko; 14. A class of quantum Zariski geometries Boris Zilber; 15. Model theory guidance in number theory? Ivan Fesenko

• ISBN: 978-0-521-69484-1
• Editorial: Cambridge University Press
• Encuadernacion: Rústica
• Páginas: 350
• Fecha Publicación: 22/05/2008
• Nº Volúmenes: 1
• Idioma: Inglés