Nelson algebras through Heyting ones: I

Studia Logica 49 (1):105-126 (1990)

Abstract
The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H
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DOI 10.1007/BF00401557
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References found in this work BETA

An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.

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Citations of this work BETA

On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
Knowledge, Uncertainty and Ignorance in Logic: Bilattices and Beyond.George Gargov - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):195-283.

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