A note on interpretations of Heyting algebras
type: Item
instance of: scholarly article
title: A note on interpretations of Heyting algebras
zbMATH Open document ID: 0642.06008
DOI: 10.1007/BF01195268
author: Walter Taylor
published in: Algebra Universalis
publication date: 1987-01-01T00:00:00Z
review text: We say that a variety V is interpretable in a variety W iff for each V- operation \(F_ t(x_ 1,...,x_ n)\) there exists a W-term \(f_ t(x_ 1,...,x_ n)\) such that if \(A=<A;G_ s>_{s\in S}\in W,\) then \(<A;f^ A_ t>\in V\). For any integer \(n\geq 2\), let \(H_ n\) be the n-element chain considered as a Heyting algebra, and let \(V_ n\) be the variety generated by \(H_ n\). Then \(V_{n+1}\) is interpretable in \(V_ n\). The author proves that \(V_ n\) is not interpretable in \(V_{n+1}\), thus giving rise to a decreasing sequence \(V_ 2>V_ 3>..\). in the lattice of interpretability types.
reviewed by: C. S. Hoo
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 08B99
zbMATH DE Number: 4045809
zbMATH Keywords: n-element chain
zbMATH Keywords: Heyting algebra
zbMATH Keywords: lattice of interpretability types
MaRDI profile type: Publication
cites work: The lattice of interpretability types of varieties
cites work: Interpretations into Heyting algebras
cites work: On Malcev conditions
description: scientific article; zbMATH DE number 4045809