This volume presents research by algebraists and model theorists in accessible form for advanced undergraduates or beginning graduate students studying algebra, logic, or model theory. It introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. A multi-step procedure, the method resembles a two-player game that continues indefinitely. This approach simplifies, motivates, and unifies a wide range of constructions.
Starting with an overview of basic model theory, the text examines a variety of algebraic applications, with detailed analyses of existentially closed groups of class 2. It describes the classical model-theoretic form of this method of construction, which is known as "omitting types," "forcing," or the "Henkin-Orey theorem," The final chapters are more specialized, discussing how the idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras and models of arithmetic. More than 160 exercises range from elementary drills to research-related items, with further information and examples.
Slightly corrected republication of the edition published by Cambridge University Press, Cambridge, 1985.
Availability | Usually ships in 24 to 48 hours |
ISBN 10 | 0486450171 |
ISBN 13 | 9780486450179 |
Author/Editor | Wilfrid Hodges |
Page Count | 336 |
Dimensions | 6 1/8 x 9 1/4 |