Distributive Lattices with a Negation Operator

Mathematical Logic Quarterly 45 (2):207-218 (1999)
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Abstract

In this note we introduce and study algebras of type such that is a bounded distributive lattice and ⌝ is an operator that satisfies the condition ⌝ = a ⌝ b and ⌝ 0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras of such an algebra. As an application, we will determine the Priestley spaces of quasi-Stone algebras

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10.1002/malq.19990450206

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Citations of this work

A Sahlqvist theorem for distributive modal logic.Mai Gehrke, Hideo Nagahashi & Yde Venema - 2004 - Annals of Pure and Applied Logic 131 (1-3):65-102.
Weak‐quasi‐Stone algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.
Weak-quasi-Stone algebras.Sergio A. Celani & Leonardo M. Cabrer - 2009 - Mathematical Logic Quarterly 55 (3):288-298.

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References found in this work

Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
Quasi‐Stone algebras.Nalinaxi H. Sankappanavar & Hanamantagouda P. Sankappanavar - 1993 - Mathematical Logic Quarterly 39 (1):255-268.
Semi-demorgan algebras.David Hobby - 1996 - Studia Logica 56 (1-2):151 - 183.
Distributive lattices with an operator.Alejandro Petrovich - 1996 - Studia Logica 56 (1-2):205 - 224.

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