Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Algebra Universalisarrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Algebra Universalis
Article . 1987 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1987
Data sources: zbMATH Open
versions View all 2 versions
addClaim

Interpretations into Heyting algebras

Authors: Lewin Riquelme de la Barrera, Renato Alfredo;

Interpretations into Heyting algebras

Abstract

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.

Country
Chile
Keywords

interpretations, variety of bounded distributive lattices, Matemática física y química, Heyting algebras (lattice-theoretic aspects), variety of Heyting algebras, Varieties of lattices, Lógica algebraica, Álgebra de BooleÁlgebra universal, 510

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    5
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!