Model Theory with Applications to Algebra and Analysis: Volume 1

Model Theory with Applications to Algebra and Analysis: Volume 1

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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 6 b/w illus.
  • 1139238973
  • 9781139238977

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 Rossler; 5. On the definitions of Difference Galois Groups Zoe 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 Kahler 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.show more

About Zoe Chatzidakis

Zoe Chatzidakis is Directeur de recherches in the Centre National de la Recherche Scientifique (CNRS) at the Universite de Paris VII. Dugald Macpherson is a Professor in the School of Mathematics at the University of Leeds. Anand Pillay is a Professor in the School of Mathematics at the University of Leeds and Swanlund Chair Emeritus in the Mathematics Department at the University of Illinois. Alex Wilkie is Fielden Professor of Pure Mathematics at the University of Manchester.show more

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