Models and games
著者
書誌事項
Models and games
（Cambridge studies in advanced mathematics, 132）
Cambridge University Press, 2011
- : hardback
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注記
Includes bibliographical references (p. [353]-361) and index
内容説明・目次
内容説明
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.
目次
- 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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