Nelson algebras through Heyting ones. I
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?
scientific article; zbMATH DE number 4174993