Abstract
The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Berman, Distributive lattices with an additional unary operation, Preprint.
J. Berman and P. Dwinger, De Morgan algebras: free products and free algebras, Preprint.
G. Grätzer, Lattice theory, Freeman and Co., San Francisco (1971).
P. Halmos, Lectures on Boolean algebras, Van Nostrand, Princeton (1963).
W. Kneale and M. Kneale, The Development of logic, Oxford University Press, Oxford (1962).
H. Priestley, Representation of distributive lattices by means of ordered Stone spaces, The Bulletin of the London Mathematical Society 2 (1970), 186–190.
H. Rasiowa, An algebraic approach to non-classical logics, North-Holland, Amsterdam (1974).
A. R. Anderson and N. D. Belnap Jr., Entailment, Princeton University Press, 1975.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Urquhart, A. Distributive lattices with a dual homomorphic operation. Stud Logica 38, 201–209 (1979). https://doi.org/10.1007/BF00370442
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370442