An explicit Kuznetsov-Muravitsky enrichment

TL;DR

This paper constructs an embedding of any Heyting algebra into a Kuznetsov-Muravitsky algebra reduct, demonstrating that this reduct generates the original Heyting algebra variety, thus linking these algebraic structures.

Contribution

It provides an explicit embedding method of Heyting algebras into Kuznetsov-Muravitsky algebras and proves the generated variety relationship.

Findings

Embedding of arbitrary Heyting algebra into Kuznetsov-Muravitsky algebra reduct

Algebraic proof of reduct belonging to Heyting algebra variety

Reduct generates the original Heyting algebra variety

Abstract

An embedding of arbitrary Heyting algebra H into a reduct from the variety of Kuznetsov-Muravitsky algebras is constructed. An algebraic proof is given that this reduct belongs to the variety of Heyting algebras generated by H.