© 2017

Introduction to Relation Algebras

Relation Algebras, Volume 1


Table of contents

  1. Front Matter
    Pages i-xxxii
  2. Steven Givant
    Pages 1-34
  3. Steven Givant
    Pages 35-69
  4. Steven Givant
    Pages 71-112
  5. Steven Givant
    Pages 113-139
  6. Steven Givant
    Pages 141-228
  7. Steven Givant
    Pages 229-270
  8. Steven Givant
    Pages 271-311
  9. Steven Givant
    Pages 313-383
  10. Steven Givant
    Pages 385-401
  11. Steven Givant
    Pages 403-418
  12. Steven Givant
    Pages 419-498
  13. Steven Givant
    Pages 499-518
  14. Steven Givant
    Pages 519-539
  15. Back Matter
    Pages 541-572

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.


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

Authors and affiliations

  1. 1.Department of MathematicsMills CollegeOaklandUSA

About the authors

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


“The intended audience of the book includes both graduate students and professionals in logic and philosophy, in computer science and, of course, in various mathematical disciplines. … The book can be used for independent study, as it is self-contained, the basic definitions are carefully given, the goals in every section are largely explained, and the principal results are given full proofs. It will be useful also as a reference book on relation algebras.” (Jānis Cīrulis, zbMATH 1426.03001, 2020)