Interpretations into Heyting algebras
type: Item
instance of: scholarly article
title: Interpretations into Heyting algebras
zbMATH Open document ID: 0614.06009
DOI: 10.1007/BF01188392
published in: Algebra Universalis
publication date: 1987-01-01T00:00:00Z
review text: A variety \({\mathcal V}\) is interpretable in a variety \({\mathcal W}\) if for each \({\mathcal V}\)-operation \(F_ t(x_ 1,...,x_ n)\) there is a \({\mathcal W}\)- term \(f_ t(x_ 1,...,x_ n)\) such that if \((A;G_ s)\) is in \({\mathcal W}\), then \((A;f^ A_ t)\) is in \({\mathcal V}\). In this paper we prove that there are only two interpretations from the variety of bounded distributive lattices into the variety of Heyting algebras, namely, the identity interpretation and its dual. As a corollary there is only one interpretation from the variety of Heyting algebras into itself. The method used is by successively showing that the result holds for larger and larger subvarieties of Heyting algebras.
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3993653
zbMATH Keywords: interpretations
zbMATH Keywords: variety of bounded distributive lattices
zbMATH Keywords: variety of Heyting algebras
author: R. A. Lewin
MaRDI profile type: Publication
cites work: On closed elements in closure algebras
cites work: On formulas of one variable in intuitionistic propositional calculus
description: scientific article; zbMATH DE number 3993653