Model theory with applications to algebra and analysis / Zoé Chatzidakis ... [and others].

Format:

• Book

Contributor:

• Chatzidakis, Zoé Maria.

Series:

• London Mathematical Society lecture note series ; 349-350.
• London Mathematical Society lecture note series ; 349-350

Language:

English

Subjects (All):

• Model theory.

Physical Description:

2 volumes : illustrations ; 23 cm.

Other Title:

Model theory and applications to algebra and analysis

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2008.

Summary:

• 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 inspired by subjects discussed at 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.

Contents:

• Conjugacy in groups of finite Morley rank / Olivier Frecon, Eric Jaligot 1
• Permutation groups of finite Morley rank / Alexandre Borovik, Gregory Cherlin 59
• A survey of asymptotic classes and measurable structures / Richard Elwes, Dugald Macpherson 125
• Counting and dimensions / Ehud Hrushovski, Frank Wagner 161
• A survey on groups definable in o-minimal structures / Margarita Otero 177
• Decision problems in Algebra and analogues of Hilbert's tenth problem / Thanases Pheidas, Karim Zahidi 207
• Hilbert's Tenth Problem for function fields of characteristic zero / Kirsten Eisentrager 237
• First-order characterization of function field invariants over large fields / Bjorn Poonen, Florian Pop 255
• Nonnegative solvability of linear equations in ordered Abelian groups / Philip Scowcroft 273
• Model theory for metric structures / Itai Ben Yaacov, Alexander Berenstein, C. Ward Henson, Alexander Usvyatsov 315.

Notes:

• "The volumes grew out of the semester on 'Model Theory and Applications to Algebra and Analysis' which took place at the Isaac Newton Institute (INI), Cambridge, froim January to July 2005"--Pref.
• Includes bibliographical references.

ISBN:

• 9780521694841
• 0521694841
• 9780521709088
• 0521709083

OCLC:

212858651