Model Theory with Applications to Algebra and Analysis
by Edited by Zoé Chatzidakis , Dugald Macpherson , Anand Pillay , Alex WilkieEdition: 1st
Format: Paperback
Pub. Date: 2008-06-09
Publisher(s): Cambridge University Press
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Summary
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.
Table of Contents
| Preface | |
| List of contributors | |
| Model theory and stability theory, with applications in differential algebra and algebraic geometry | |
| Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations | |
| Schanuel's conjecture for non-isoconstant elliptic curves over function fields | |
| An afterthought on the generalized Mordell-Lang conjecture | |
| On the definitions of Difference Galois Groups ZoF | |
| Differentially valued fields are not differentially closed | |
| Complex analytic geometry in a nonstandard setting | |
| Model theory and Kahler geometry | |
| Some local definability theory for holomorphic functions | |
| Some observations about the real and imaginary parts of complex Pfaffian functions | |
| Fusion of structures of finite Morley rank | |
| Establishing the o-minimality for expansions of the real field | |
| On the tomography theorem | |
| A class of quantum Zariski geometries | |
| Model theory guidance in number theory? | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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