Building Models by Games - Couverture rigide

Hodges, Wilfrid

Couverture rigide

ISBN 10 : 0521268974 ISBN 13 : 9780521268974

Editeur : Cambridge University Press, 1985

A propos du livre

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.

À propos de cette édition

• Éditeur: Cambridge University Press
• Date d'édition: 1985
• ISBN 10: 0521268974
• ISBN 13: 9780521268974
• Reliure: Relié
• Numéro d'édition: 1
• Nombre de pages: 320