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Model Theory in Algebra, Analysis and Arithmetic

Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori

  • Book
  • © 2014

Overview

Authors:
  1. Lou Dries

    1. Department of Mathematics, University of Illinois, Urbana, USA

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  2. Jochen Koenigsmann

    1. Mathematical Institute, University of Oxford, Oxford, United Kingdom

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  3. H. Dugald Macpherson

    1. University of Leeds School of Mathematics, Leeds, United Kingdom

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  4. Anand Pillay

    1. Department of Mathematics, University of Notre Dame, Hurley, USA

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  5. Carlo Toffalori

    1. Division of Mathematics, University of Camerino School of Science and Technology, Camerino, Italy

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  6. Alex J. Wilkie

    1. University of Manchester School of Mathematics, Manchester, United Kingdom

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  • Presentation of a seminar result (Wilkie's o-minimality of the real exponential field) through a series of exercises
  • Extended expository article on the model theory of valued fields, an area with many current researchers and a lack of good expositions
  • Wide-ranging and up-to-date overview of undecidability and Hilbert's Tenth Problem, linking model theory, number theory, and algebraic geometry
  • Exposition of recent breakthrough in abstract model theory, around NIP theories

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2111)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-vii
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  2. Model Theory in Algebra, Analysis and Arithmetic: A Preface

    • Dugald Macpherson, Carlo Toffalori
    Pages 1-11

  3. Some Themes Around First Order Theories Without the Independence Property

    • Anand Pillay
    Pages 13-33

  4. Lectures on the Model Theory of Real and Complex Exponentiation

    • A. J. Wilkie
    Pages 35-53

  5. Lectures on the Model Theory of Valued Fields

    • Lou van den Dries
    Pages 55-157

  6. Undecidability in Number Theory

    • Jochen Koenigsmann
    Pages 159-195

  7. Back Matter

    Pages 197-198
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Keywords

About this book

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana, USA

    Lou Dries

  • Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Jochen Koenigsmann

  • University of Leeds School of Mathematics, Leeds, United Kingdom

    H. Dugald Macpherson

  • Department of Mathematics, University of Notre Dame, Hurley, USA

    Anand Pillay

  • Division of Mathematics, University of Camerino School of Science and Technology, Camerino, Italy

    Carlo Toffalori

  • University of Manchester School of Mathematics, Manchester, United Kingdom

    Alex J. Wilkie

Bibliographic Information

  • Book Title: Model Theory in Algebra, Analysis and Arithmetic

  • Book Subtitle: Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori

  • Authors: Lou Dries, Jochen Koenigsmann, H. Dugald Macpherson, Anand Pillay, Carlo Toffalori, Alex J. Wilkie

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-54936-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2014

  • Softcover ISBN: 978-3-642-54935-9Published: 02 October 2014

  • eBook ISBN: 978-3-642-54936-6Published: 20 September 2014

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VII, 195

  • Topics: Mathematical Logic and Foundations, Algebra, Analysis, Number Theory

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