Ockham algebras--the natural generalization of a well known and important notion of a boolean algebra--has an infinite amount of subvarieties, including those of de Morgan, Stone, and Kleene algebras. This book, the first unified account of the subject, details the many important breakthroughs that have occurred in this area of lattice theory since Berman's pioneering work in 1977. Particular emphasis is placed on Priestley's topological duality, which involves ordered sets and order-reversing maps. With its many illustrative examples and substantial bibliography, Ockham Algebras is the perfect introduction to the subject for graduate students and researchers studying algebra and lattice theory.

• Ordered sets, lattices, and universal algebra


• 1: Examples of Ockham algebras, the Berman classes


• 2: Congruence relations


• 3: Subdirectly irreducible algebras


• 4: Duality theory


• 5: The lattice of subvarieties


• 6: Fixed points


• 7: Fixed point separating congruences


• 8: Congruences on K1.1-algebras


• 9: MS-spaces; fences, crowns, ...


• 10: The dual space of a finite simples Ockham algebra


• 11: Relative Ockham algebras


• 12: Double MS-algebras


• 13: Subdirectly irreducible double MS-algebras


• 14: Congruences on double MS-algebras


• 15: Singles and doubles


• Bibliography


• Notation index


• Index