Bounded depth in Hilbert algebras

TL;DR

This paper demonstrates that the property of having bounded depth in Hilbert algebras can be characterized by an equational condition, extending a known result from Heyting algebras.

Contribution

It establishes that bounded depth is an equational property in Hilbert algebras, generalizing a classical result from Heyting algebra theory.

Findings

Bounded depth is characterized by an equational condition in Hilbert algebras.

This result generalizes a known property from Heyting algebras.

The paper provides a new algebraic characterization of depth in Hilbert algebras.

Abstract

Hilbert algebras are the implicative subreducts of Heyting algebras. It is shown that having depth at most n is an equational condition in Hilbert algebras. This generalizes an analogous well-known result in the setting of Heyting algebras.