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Models and Games

$81.95 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: May 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521518123

$ 81.95 (C)

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About the Authors
  • This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.

    • The first graduate-level text with a game-theoretic viewpoint
    • A gentle introduction spanning the very basic to the cutting edge
    • Contains over 500 exercises
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    Reviews & endorsements

    "This is a very valuable book, written by a highly competent logician and mathematician who has himself contributed to the field. Parts of it (roughly, chapters 1 to 7) can be used in an introductory course in model theory with a game-theoretical flavor. The last two or three chapters, however, will require a bit more mathematical bravery, but the effort pays off."
    Walter Carnielli, Computing Reviews

    "The strength of the book is the validation of a game-theoretical approach to logic. The interdisciplinary value of such an approach is unquestionable. The book provides a significant reference not only for logicians, set-theorists and, by default, game-theorists, but also for whoever may be interested in novel applications to more applied fields."
    Debora Di Caprio and Francisco J. Santos-Arteaga, Mathematical Reviews

    "… original and very ambitious … covers a remarkable amount of material, much in the main text and even more in over 500 exercises."
    The Mathematical Intelligencer

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    Product details

    • Date Published: May 2011
    • format: Hardback
    • isbn: 9780521518123
    • length: 380 pages
    • dimensions: 229 x 152 x 25 mm
    • weight: 0.73kg
    • contains: 120 b/w illus. 560 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Preliminaries and notation
    3. Games
    4. Graphs
    5. Models
    6. First order logic
    7. Infinitary logic
    8. Model theory of infinitary logic
    9. Stronger infinitary logics
    10. Generalized quantifiers

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    Models and Games

    Jouko Väänänen

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  • Author

    Jouko Väänänen, University of Helsinki and University of Amsterdam
    Jouko Väänänen is a Professor of Mathematics at the University of Helsinki, and a Professor of Mathematical Logic and Foundations of Mathematics at the University of Amsterdam.

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