Models and Ultraproducts: An Introduction (Dover Books on Mathematics)

Book Details:

• Publisher: Dover

• Author: J L Bell

• Language: English

• Edition: Illustrated Edition

• ISBN: 9780486449791

• Pages: 336

• Binding: Paperback

• Release Date: 26-05-2006

• Package Dimensions: 8.4 x 5.4 x 0.7 inches

About The Book:

Model Theory: An Introduction by J L Bell is an accessible and thorough introduction to the fundamental concepts of model theory, making it ideal for first-year graduate students. The book focuses on the ultraproduct construction, offering a detailed examination of its properties and the areas in which it is most useful.

Beginning with foundational topics such as Boolean algebra, propositional calculus, and predicate calculus, the book then delves into the core of model theory. The fourth chapter introduces model theory proper, with in-depth discussions on ultraproduct construction, elementary equivalence, and algebraic descriptions of elementary classes.

The text also covers completeness, as well as key results from the works of Jónsson, Morley, and Vaught on homogeneous universal models, and Keisler’s contributions to the concept of saturated structures. Classical results from Gödel and Skolem are explored, and the book extends classical first-order logic to include generalized quantifiers and infinitary languages.

With numerous exercises throughout, Model Theory: An Introduction offers both theoretical insights and practical problems to reinforce understanding, making it an invaluable resource for students in logic and mathematical theory.