
doi: 10.1007/bf01188392
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.
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
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
| 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 |
