Models and Games

This introductory text clearly presents three important games in logic, from the basics to the cutting edge.

Jouko Väänänen (Author)

9780521518123, Cambridge University Press

Hardback, published 5 May 2011

380 pages, 120 b/w illus. 560 exercises
22.9 x 15.2 x 2.5 cm, 0.73 kg

'… 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

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.

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.

Subject Areas: Game theory [PBUD], Mathematical logic [PBCD]