Model Theory with Applications to Algebra and Analysis
Model Theory with Applications to Algebra and Analysis
Dugald Macpherson, University of Leeds
Anand Pillay, University of Leeds
Alex Wilkie, University of Manchester
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$70.00
(C) USDThe 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.
- 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
Product details
May 2012Adobe eBook Reader
9781139238977
0 pages
0kg
6 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
