Nelson algebras through Heyting ones. I
type: Item
instance of: scholarly article
title: Nelson algebras through Heyting ones. I
zbMATH Open document ID: 0714.06004
DOI: 10.1007/BF00401557
author: Andrzej Sendlewski
published in: Studia Logica
publication date: 1990-01-01T00:00:00Z
review text: For any Nelson algebra N the relation E on N defined by the rule E(a,b) iff \(a\to b=1\) and \(b\to a=1\) is a congruence relation on the algebra N and the quotient algebra \(N/E=N^*\) is a Heyting algebra. Each Heyting algebra H can be represented up to isomorphism as \(N^*\) for some Nelson algebra N. The author positively solves the following problems: Problem 1. Find a useful and possibly simple description (construction) of all (up to isomorphism) Nelson algebras N whose Heyting algebras \(N^*\) are isomorphic to a given Heyting algebra H. Problem 2. Is it possible to apply the obtained description to state connections between varieties (quasivarieties) of Nelson and Heyting algebras?
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D30
zbMATH DE Number: 4174993
zbMATH Keywords: Priestley's duality
zbMATH Keywords: Nelson algebra
zbMATH Keywords: congruence
zbMATH Keywords: quotient algebra
zbMATH Keywords: Heyting algebra
reviewed by: Leo Esakia
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00401557
OpenAlex ID: W2053168571
description: scientific article; zbMATH DE number 4174993