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Cambridge Studies in Advanced Mathematics Models and Games

by Jouko Vaananen

Cambridge Studies in Advanced Mathematics Models and Games Synopsis

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.

Cambridge Studies in Advanced Mathematics Models and Games Press Reviews

'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 Intelligencer 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

Book Information

ISBN: 9780521518123
Publication date: 5th May 2011
Author: Jouko Vaananen
Publisher: Cambridge University Press
Format: Hardback
Pagination: 380 pages
Categories: Game theory, Mathematical logic,

About Jouko Vaananen

Jouko Vaananen 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.

More About Jouko Vaananen

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