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Models and games

Vaananen, J. (1950-)

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Models and games

Record Type:	Electronic resources : Monograph/item
Title/Author:	Models and games/ Jouko Vaananen.
remainder title:	Models & Games
Author:	Vaananen, J.
Published:	Cambridge :Cambridge University Press, : 2011.,
Description:	ix, 367 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers.
Subject:	Model theory. -
Online resource:	https://doi.org/10.1017/CBO9780511974885
ISBN:	9780511974885

Models and games
Vaananen, J.1950-

Models and games[electronic resource] /Models & GamesJouko Vaananen. - Cambridge :Cambridge University Press,2011. - ix, 367 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;132. - Cambridge studies in advanced mathematics ;132..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers.

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.

ISBN: 9780511974885Subjects--Topical Terms:

560899
Model theory.

LC Class. No.: QA9.7 / .V33 2011

Dewey Class. No.: 511.34

Models and games
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245 1 0 $a Models and games $h [electronic resource] / $c Jouko Vaananen.
246 3 $a Models & Games
260 $a Cambridge : $b Cambridge University Press, $c 2011.
300 $a ix, 367 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 132
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Introduction -- Preliminaries and notation -- Games -- Graphs -- Models -- First-order logic -- Infinitary logic -- Model theory of infinitary logic -- Stronger infinitary logics -- Generalized quantifiers.
520 $a 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.
650 0 $a Model theory. $3 560899
830 0 $a Cambridge studies in advanced mathematics ; $v 132. $3 3470399
856 4 0 $u https://doi.org/10.1017/CBO9780511974885