Building models by games
Author(s)
Bibliographic Information
Building models by games
（London Mathematical Society student texts, 2）
Cambridge University Press, 1985
- : hard
- : pbk
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardHOD||3||185023026
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Note
Bibliography: p. 282-302
Includes index
Description and Table of Contents
Description
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.
by "Nielsen BookData"