Studia Logica 56 (1-2):205 - 224 (1996)

It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences.
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DOI 10.1007/BF00370147
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References found in this work BETA

The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.

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Citations of this work BETA

Bounded Distributive Lattices with Strict Implication.Sergio Celani & Ramon Jansana - 2005 - Mathematical Logic Quarterly 51 (3):219-246.
Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - Mathematical Logic Quarterly 45 (2):207-218.
Independence-Friendly Cylindric Set Algebras.Allen Mann - 2009 - Logic Journal of the IGPL 17 (6):719-754.

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