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A Guide to NIP Theories


Part of Lecture Notes in Logic

  • Date Published: July 2015
  • availability: Available
  • format: Hardback
  • isbn: 9781107057753

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About the Authors
  • The study of NIP theories has received much attention from model theorists in the last decade, fuelled by applications to o-minimal structures and valued fields. This book, the first to be written on NIP theories, is an introduction to the subject that will appeal to anyone interested in model theory: graduate students and researchers in the field, as well as those in nearby areas such as combinatorics and algebraic geometry. Without dwelling on any one particular topic, it covers all of the basic notions and gives the reader the tools needed to pursue research in this area. An effort has been made in each chapter to give a concise and elegant path to the main results and to stress the most useful ideas. Particular emphasis is put on honest definitions, handling of indiscernible sequences and measures. The relevant material from other fields of mathematics is made accessible to the logician.

    • The first book devoted to NIP theories
    • A concise introduction that provides enough background material to understand current research in the area
    • Contains over 50 exercises and pointers to additional topics to help readers progress further
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    Reviews & endorsements

    'This book presents NIP theories as a rich and coherent subject, showing a field with a considerable degree of development, particularly taking into account how recent most of the results are. Also, the author made a clear effort in presenting the most elegant proofs he could find, making this a very valuable book and accessible for any reader who understands model theory …' Alf Onshuus, Mathematical Reviews

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    Product details

    • Date Published: July 2015
    • format: Hardback
    • isbn: 9781107057753
    • length: 166 pages
    • dimensions: 236 x 160 x 18 mm
    • weight: 0.4kg
    • contains: 50 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    2. The NIP property and invariant types
    3. Honest definitions and applications
    4. Strong dependence and dp-ranks
    5. Forking
    6. Finite combinatorics
    7. Measures
    8. Definably amenable groups
    9. Distality
    Appendix A. Examples of NIP structures
    Appendix B. Probability theory

  • Author

    Pierre Simon, Université Lyon I
    Pierre Simon is Chargé de recherche, CNRS, at Université Lyon 1, France. He completed his PhD at Université Paris-Sud, Orsay under the supervision of Elisabeth Bourscaren. His thesis, 'Ordre et stabilité dans les théories NIP', received the 2012 Sacks Prize for the best thesis in logic that year as well as the Perrissin-Pirasset/Schneider prize from the Chancellerie des Universités de Paris.

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