Model Theory with Applications to Algebra and Analysis: Volume 1

Account of current research in model theory and its connections with algebra and analysis; contributions from leaders in the field.

Zoé Chatzidakis (Edited by), Dugald Macpherson (Edited by), Anand Pillay (Edited by), Alex Wilkie (Edited by)

9780521694841, Cambridge University Press

Paperback, published 22 May 2008

352 pages, 6 b/w illus.
22.9 x 15.2 x 1.8 cm, 0.48 kg

The first 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. Each volume contains 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 convey 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 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.

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.

Subject Areas: Mathematical foundations [PBC]