Hereditarily Structurally Complete Superintuitionistic Logics and Primitive Varieties of Heyting Algebras

TL;DR

This paper provides an algebraic criterion to determine when an intermediate logic is hereditarily structurally complete, linking it to the primitiveness of certain varieties of Heyting algebras, thus advancing the algebraic understanding of these logics.

Contribution

It introduces an algebraic proof for the criterion of hereditary structural completeness in intermediate logics, connecting it to primitive varieties of Heyting algebras.

Findings

Algebraic criterion for hereditary structural completeness

Equivalence between hereditary structural completeness and primitiveness of Heyting algebra varieties

Enhanced understanding of the algebraic structure of intermediate logics

Abstract

We give an algebraic proof of the criterion for hereditary structural completeness of an intermediate logic, or, equivalently, of the primitiveness of a variety of Heyting algebras.