Models and Games

Models and Games

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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-Fraisse 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 Vaananen 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.
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Product details

  • Electronic book text | 380 pages
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 120 b/w illus. 560 exercises
  • 9781139064736

Table of contents

Preface; 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; References; Index.
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Review quote

'The book can be used for reference purposes, as well as for teaching and self-study at the graduate level. It is a welcome addition to the literature on game-theoretic model theory.' Daniele Mundici, Zentralblatt MATH '... an interesting book that, while written by a logician, has lots of things to offer to computer scientists with theoretical inclinations.' Panos Rondogiannis, Theory and Practice of Logic Programming '... 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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About Jouko Väänänen

Jouko Vaananen 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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