Models and Games

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Cambridge University Press, May 5, 2011 - Mathematics
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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–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.
 

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Contents

Introduction
1
Games
14
Graphs
35
Models
53
FirstOrder Logic
79
Infinitary Logic
139
Model Theory of Infinitary Logic
176
1
183
Stronger Infinitary Logics
228
Exercises
278
Exercises
343
References
353
Index
362
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About the author (2011)

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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