Overview
Introduces readers from mathematics, computer science, and beyond to the increasingly relevant field of relation algebras
Engages the reader with numerous examples, exercises, and historical remarks
The first volume of a textbook pair, which together provide a landmark unified treatment of the field
Includes supplementary material: sn.pub/extras
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Table of contents (13 chapters)
Keywords
- Relation algebras
- Arithmetic of relation algebras
- Special elements in relation algebras
- Subalgebras of relation algebras
- Relativizations of relation algebras
- Steven Givant relation algebras
- Alfred Tarski relation algebras
- Equational language of relation algebras
- Elementary theory of binary relations
- Homomorphisms
- Constructing new relation algebras
About this book
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field.
The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field.
Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.
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Authors and Affiliations
About the author
Steven Givant is a Professor of Mathematics and Computer Science at Mills College, California. As a long-term collaborator of Alfred Tarski—one of the great logicians—Givant has been involved first-hand in the development of the field of relation algebras since the 1970s. His previous books include Duality Theories for Boolean Algebras with Operators (Springer, 2014), Introduction to Boolean Algebras, with Paul Halmos (Springer, 2009), Logic as Algebra, with Paul Halmos (MAA, 1998), and A Formalization of Set Theory without Variables, with Alfred Tarski (AMS, 1987). He was also coeditor, with Ralph McKenzie, of Alfred Tarski's Collected Papers: Vol 1-4 (Birkhäuser, 1986).
Bibliographic Information
Book Title: Introduction to Relation Algebras
Book Subtitle: Relation Algebras, Volume 1
Authors: Steven Givant
DOI: https://doi.org/10.1007/978-3-319-65235-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-65234-4Published: 14 September 2017
Softcover ISBN: 978-3-319-87981-9Published: 12 August 2018
eBook ISBN: 978-3-319-65235-1Published: 29 August 2017
Edition Number: 1
Number of Pages: XXXII, 572
Number of Illustrations: 25 b/w illustrations
Topics: Mathematical Logic and Foundations, General Algebraic Systems