An Ockham algebra is a natural generalization of a well known and
important notion of a boolean algebra. Regarding the latter as a
bounded distributive lattice with complementation (a dual
automorphism of period 2) by a dual endomorphism that satisfies the
de Morgan laws, this seemingly modest generalization turns out to
be extemely wide. The variety of Ockham algebras has infinitely
many subvarieties including those of de Morgan algebras, Stone
algebras, and Kleene algebras. Folowing pioneering work by Berman
in 1977, many papers have appeared in this area oflattice theory to
which several important results in the theory of universal algebra
are highly applicable. This is the first unified account of some of
this research. Particular emphasis is placed on Priestly's
topological duality, which invloves working with ordered sets and
order-reversing maps, hereby involving many problems of a
combinatorial nature. Written with the graduate student in mind,
this book provides an ideal overview of this are of increasing
interest.
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