Models and Games
1st Edition
Published on 26. May 2011
978-1-139-06473-6 (ISBN)
Description
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 Vaeaenaenen 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.
Reviews / Votes
'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 IntelligencerMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 25 Halftones, unspecified; 95 Line drawings, unspecified
File size
6,67 MB
ISBN-13
978-1-139-06473-6 (9781139064736)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Jouko Vaeaenaenen
Models and Games
Book
05/2011
Cambridge University Press
€98.00
Shipment within 15-20 days
Person
Jouko Vaeaenaenen 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.
Content
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.
