Injectives in the variety generated by a finite subdirectly irreducible Heyting algebra with involution

TL;DR

This paper characterizes injective algebras in the variety generated by finite subdirectly irreducible Heyting algebras with involution, showing they are exactly certain complete diagonal subalgebras of direct powers.

Contribution

It proves finite subdirectly irreducible Heyting algebras with involution are quasi-primal and characterizes their injective algebras explicitly.

Findings

Injective algebras are complete diagonal subalgebras of direct powers.

Finite subdirectly irreducible Heyting algebras with involution are quasi-primal.

Characterization of injectives in the generated variety.

Abstract

We prove that any finite subdirectly irreducible Heyting algebra with involution is quasi-primal, and that injective algebras in the variety generated by a finite subdirectly irreducible Heyting algebra are precisely diagonal subalgebras of some direct power of this algebra, which are complete as lattices.