Models and games / Jouko Väänänen.

Format:

Book

Author/Creator:

Väänänen, J. (Jouko), 1950- author.

Series:

Cambridge studies in advanced mathematics ; 132.

Cambridge studies in advanced mathematics ; 132

Language:

English

Subjects (All):

Model theory.

Physical Description:

1 online resource (ix, 367 pages) : digital, PDF file(s).

Other Title:

Models & Games

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

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.

Contents:

Introduction

Preliminaries and notation

Games

Graphs

Models

First-order logic

Infinitary logic

Model theory of infinitary logic

Stronger infinitary logics

Generalized quantifiers.

Notes:

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

Includes bibliographical references and index.

ISBN:

1-107-21603-6

1-283-11881-5

9786613118813

1-139-07508-X

1-139-06931-4

1-139-07734-1

1-139-07962-X

0-511-97488-4

1-139-08190-X

OCLC:

729166634