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

Slomson, A. B.; Bell, J. L.

Softcover

ISBN 10: 0486449793 ISBN 13: 9780486449791

Publisher: Dover Publications, 2006

Synopsis

In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus.
Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.

About this title

About the Author

John L. Bell is a Professor of Philosophy at the University of Western Ontario and Alan Slomson is Director of Undergraduate Studies at the University of Leeds' School of Mathematics.

Edition details

• Publisher: Dover Publications
• Publication date: 2006
• ISBN 10: 0486449793
• ISBN 13: 9780486449791
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 336