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Model Theory with Applications to Algebra and Analysis

Volume 1

£43.99

Part of London Mathematical Society Lecture Note Series

Anand Pillay, Daniel Bertrand, Damian Rössler, Zoé Chatzidakis, Charlotte Hardouin, Michael F. Singer, Thomas Scanlon, Ya'acov Peterzil, Sergei Starchenko, Rahim Moosa, A. J. Wilkie, Angus Macintyre, Martin Ziegler, Jean-Philippe Rolin, Boris Zilber, Ivan Fesenko
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  • Date Published: May 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521694841

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About the Authors
  • 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.

    • 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
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    Product details

    • Date Published: May 2008
    • format: Paperback
    • isbn: 9780521694841
    • length: 352 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.48kg
    • contains: 6 b/w illus.
    • availability: Available
  • 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.

  • Editors

    Zoé Chatzidakis, Centre National de la Recherche Scientifique (CNRS), Paris
    Zoé Chatzidakis is Directeur de recherches in the Centre National de la Recherche Scientifique (CNRS) at the Université de Paris VII.

    Dugald Macpherson, University of Leeds
    Dugald Macpherson is a Professor in the School of Mathematics at the University of Leeds.

    Anand Pillay, 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, University of Manchester
    Alex Wilkie is Fielden Professor of Pure Mathematics at the University of Manchester.

    Contributors

    Anand Pillay, Daniel Bertrand, Damian Rössler, Zoé Chatzidakis, Charlotte Hardouin, Michael F. Singer, Thomas Scanlon, Ya'acov Peterzil, Sergei Starchenko, Rahim Moosa, A. J. Wilkie, Angus Macintyre, Martin Ziegler, Jean-Philippe Rolin, Boris Zilber, Ivan Fesenko

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