In this new text, Steven Givantthe author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarskidevelops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.

Present three theories of duality for Boolean algebras with operators Features new results concerning the duality between various classes of Boolean algebras and classes of relational structures Gathers together into a unified framework a number of disparate results appearing in the literature Includes supplementary material: sn.pub/extras

Autorentext

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).

Inhalt

1. Algebraic Duality.- 2. Topological Duality.- 3. Hybrid Duality.