Model theory with applications to algebra and analysis

Author(s)

• Chatzidakis, Zoé Maria

Bibliographic Information

Model theory with applications to algebra and analysis

[edited by] Zoé Chatzidakis ... [et al.]

（London Mathematical Society lecture note series, 349-350）

Cambridge University Press, 2008

• v. 1
• v. 2

Note

Includes bibliographical references

Description and Table of Contents

Volume

v. 1 ISBN 9780521694841

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.

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 Roessler
• 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.

Volume

v. 2 ISBN 9780521709088

Description

The second 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 non-commutative 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.

Table of Contents

• Preface
• List of contributors
• 1. Conjugacy in groups of finite Morley rank Olivier Frecon and Eric Jaligot
• 2. Permutation groups of finite Morley rank Alexandre Borovik and Gregory Cherlin
• 3. A survey of asymptotic classes and measurable structures Richard Elwes and Dugald Macpherson
• 4. Counting and dimensions Ehud Hrushovski and Frank Wagner
• 5. A survey on groups definable in o-minimal structures Margarita Otero
• 6. Decision problems in algebra and analogues of Hilbert's tenth problem Thanases Pheidas and Karim Zahidi
• 7. Hilbert's tenth problem for function fields of characteristic zero Kirsten Eisentrager
• 8. First-order characterization of function field invariants over large fields Bjorn Poonen and Florian Pop
• 9. Nonnegative solvability of linear equations in ordered Abelian groups Philip Scowcroft
• 10. Model theory for metric structures IItai Ben Yaacov, Alexander Berenstein, C. Ward Henson and Alexander Usvyatsov.

by "Nielsen BookData"

Details

• NCID: BA85811752
• ISBN:
  • 9780521694841
  • 9780521709088
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge, UK
• Pages/Volumes: 2 v.
• Size: 23 cm
• Parent Bibliography ID:
  • BA0005393X