Simple Relation Algebras

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 other books include Introduction to Relation Algebras and Advanced Topics in Relation Algebras (Springer, 2017), 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 a coeditor, with Ralph McKenzie, of the collected papers of Alfred Tarski (Birkhäuser, 1986). Hajnal Andréka is a Professor of Mathematics at the Alfréd Rényi Institute of Mathematics in the Hungarian Academy of Sciences. She has been a prominentfigure in the development of relation algebra theory since the 1970s and won the prestigious Alfréd Rényi Prize in 1987. Her other books include Universal Algebraic Logic, with István Németi and Ildikó Sain (Birkhäuser, 2017), Decision Problems for Equational Theories of Relation Algebras, with Steven Givant and István Németi (AMS, 1997), and Cylindric Set Algebras, with Leon Henkin, J. Donald Monk, Alfred Tarski, and István Németi (Springer, 1981).

• Preface.- 1. Rectangular Semiproducts.- 2. Equivalence Semiproducts.- 3. Diagonal Semiproducts.- 4. Semipowers.- 5. Simple Closures.- 6. Quasi-bijective Relation Algebras.- 7. Quotient Relations Algebras and Equijections.- 8. Quotient Semiproducts.- 9. Group and Geometric Quotient Semiproducts.- 10. Insertion Semiproducts.- 11. Two-quasi-bijective Relation Algebras.- A. Relation Algebras.- B. Geometry.- C. Selected Hints to Exercises.- References.