Relation Algebras

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. 


This set charts relation algebras from novice to expert level. The first volume, Introduction to Relation Algebras, offers a comprehensive grounding for readers new to the topic. The second, Advanced Topics in Relation Algebras, build on this foundation and advances the reader into the deeper mathematical results of the past few decades. Such material offers an ideal preparation for research in relation algebras and Boolean algebras with operators.


Note that the second volume contains numerous, essential references to the first. Readers of the advanced material are encouraged to purchase the pair as a set, as access to the first book is necessary to make use of the second.

• Relation algebras
• canonical extensions
• representations
• atom structures
• varieties of relation algebras
• arithmetic of relation algebras
• special elements in relation algebras
• subalgebras 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

• Department of Mathematics, Mills College, Oakland, USA

  Steven Givant

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).

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