Model Theory with Applications to Algebra and Analysis: Volume 1

ISBN-13: 9780521694841 / Angielski / Miękka / 2008 / 352 str.

Opis

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.

Spis treści

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 and imaginary 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.