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Synopsis
This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.
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Présentation de l'éditeur
This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.
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Building Models by Games
Edité par
Cambridge University Press, 1985
ISBN 10 : 0521317169
ISBN 13 : 9780521317160
Ancien ou d'occasion
Couverture souple
Vendeur : Munster & Company LLC, ABAA/ILAB, Corvallis, OR, Etats-Unis
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Etat : Good. Cambridge University Press, 1985. Cover lightly rubbed/bumped, unevenly sunned, corners faintly rubbed/bumped, spine sunned, spine ends faintly rubbed/bumped; edges very lightly soiled/bumped; erasures on Title page; binding tight; cover, edges, and interior intact and clean except as noted. paperback. Good. N° de réf. du vendeur 623006
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Building Models by Games (London Mathematical Society Student Texts, Series Number 2)
Edité par
Cambridge University Press, 1985
ISBN 10 : 0521317169
ISBN 13 : 9780521317160
Ancien ou d'occasion
paperback
Vendeur : dsmbooks, Liverpool, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
paperback. Etat : Good. Good. book. N° de réf. du vendeur D8S0-3-M-0521317169-3
Quantité disponible : 1 disponible(s)
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Building Models by Games
Edité par
Cambridge Univ Pr, Cambridge, 1985
ISBN 10 : 0521317169
ISBN 13 : 9780521317160
Ancien ou d'occasion
Paper Bound
Vendeur : Feldman's Books, Menlo Park, CA, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Paper Bound. Etat : Near Fine. First Edition. N° de réf. du vendeur 00030626
Quantité disponible : 1 disponible(s)