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Nelson algebras through Heyting ones: I

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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 ([15], [16]) 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 (Thm 2.3). The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction ([6], [25]) is also given (Thm 3.6). These results are applied to compare the equational category N of Nelson algebras and some its subcategories (and their duals) with the equational category H of Heyting algebras (and its dual). It is proved (Thm 4.1) that the category N is topological over the category H.

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Authors and Affiliations

  1. Institute of Mathematics, Nicholas Copernicus University, Toruń, Poland

    Andrzej Sendlewski

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  1. Andrzej Sendlewski
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The main results of this article are a part of theses of the author's doctoral dissertation at the Nicholas Copernicus University in 1984 (cpmp. [24]).

Research partially supported by Polish Government Grant CPBP 08-15.

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Sendlewski, A. Nelson algebras through Heyting ones: I. Stud Logica 49, 105–126 (1990). https://doi.org/10.1007/BF00401557

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  • DOI: https://doi.org/10.1007/BF00401557

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