Models and Games

by Jouko Väänänen

Overview

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.

Product Details

ISBN-13:	9780521518123
Publisher:	Cambridge University Press
Publication date:	05/05/2011
Series:	Cambridge Studies in Advanced Mathematics , #132
Pages:	380
Product dimensions:	6.20(w) x 9.00(h) x 1.00(d)

About the Author

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.

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.

Editorial Reviews

"This is a very valuable book, written by a highly competent logician and mathematician who has himself contributed to the field. Parts of it (roughly, chapters 1 to 7) can be used in an introductory course in model theory with a game-theoretical flavor. The last two or three chapters, however, will require a bit more mathematical bravery, but the effort pays off."
Walter Carnielli, Computing Reviews

"The strength of the book is the validation of a game-theoretical approach to logic. The interdisciplinary value of such an approach is unquestionable. The book provides a significant reference not only for logicians, set-theorists and, by default, game-theorists, but also for whoever may be interested in novel applications to more applied fields."
Debora Di Caprio and Francisco J. Santos-Arteaga, Mathematical Reviews

"… 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

From the Publisher