Building Models by Games (Dover Books on Mathematics)

📘 Book Details

• Author: Wilfrid Hodges

• Publisher: Dover

• Language: English

• ISBN: 9780486450179

• Pages: 318

• Cover: Paperback

• Release Date: 14-04-2006

📝 About The Book

Building Infinite Structures by Wilfrid Hodges presents research in algebra and model theory in an accessible format for advanced undergraduates and beginning graduate students. The book introduces a general method for constructing infinite mathematical structures and surveys its applications in algebra and model theory. The multi-step process outlined resembles a two-player game, providing a simplified, motivated, and unified approach to a wide range of constructions.

Starting with an overview of basic model theory, the text delves into various algebraic applications, including an analysis of existentially closed groups of class 2. The book also explores the classical model-theoretic form of the construction method, known as "omitting types," "forcing," or the "Henkin-Orey theorem." The final chapters are more specialized, focusing on building uncountable structures and applications in areas such as Magidor-Malitz quantifiers, Shelah's omitting types theorem for L(Q), Boolean algebras, and models of arithmetic.

With over 160 exercises ranging from elementary drills to research-related problems, this book provides a thorough foundation and offers a wealth of further examples and information to enhance understanding.