The Structure of Relation Algebras Generated by Relativizations
The foundation of an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schroder during the second half of the nineteenth century. Modern development of the subject as a theory of abstract algebras, called "relation algebras", was undertaken by Tarski and his students. This book aims to analyse the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures (i.e., for minimal simple algebras containing a given family of relation algebras as relativized subalgebras). This book is well-written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses onalgebras of binary relations or algebraic logic.
This is an analysis of the structure of relation algebras that are generated by relativized subalgebras. The work presented here is a natural progression from that on 'relation algebras' undertaken by Tarski and his students. Throughout the text is well written and presented in an accessible way, ideal for non-specialists in this area.