Building Models by Games
Format: Hardcover
ISBN13: 9780521268974
Hardcover|9780521268974
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Overview
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.
| ISBN-13 | 9780521268974 |
|---|---|
| ISBN-10 | 0521268974 |
| List Price | $54.50 |
| Edition | 1st Edition |
| Format | Hardcover |
|---|---|
| Language | English |
| Pages | 320 pages |
| Publisher | Cambridge University Press |
| Published On | 1985-05-02 |
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