Models and games

By:

Vaananen, Jouko

Series: Cambridge studies in advanced mathematics ; 132Publication details: Cambridge University Press, 2011. Cambridge:Description: ix,367 p. : ill. ; hb, 24 cmISBN:

9780521518123

Subject(s):

DDC classification:

511.34 VAA

Summary: 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.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	511.34 VAA (Browse shelf(Opens below))	1	Available		030136

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Previous	511.32 BEL Toposes and local set theories: an introduction	511.32 PLO Hausdorff on ordered sets	511.322 BAB Write your own proofs: in set theory and discrete mathematics	511.34 VAA Models and games	511.36 WOH Introduction to proof in abstract mathematics	511.4 EVG Asymptotic estimates and entire functions	511.43 BEV Data reduction and error analysis for the physical sciences	Next

Includes bibliographical references (pages 353-361) and index.

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.

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