Counting relations on Ockham algebras

TL;DR

This paper classifies finite Ockham algebras based on the finiteness of their compatible relations, identifying two infinite families: quasi-primal Ockham algebras and generalized Stone algebras.

Contribution

It provides a complete classification of finite Ockham algebras with finitely many compatible relations, highlighting two specific algebraic families.

Findings

Two countably infinite families identified: quasi-primal Ockham algebras and generalized Stone algebras.

Finite Ockham algebras with finitely many compatible relations are fully characterized.

Classification up to isomorphism and symmetry achieved.

Abstract

We find all finite Ockham algebras that admit only finitely many compatible relations (modulo a natural equivalence). Up to isomorphism and symmetry, these Ockham algebras form two countably infinite families: one family consists of the quasi-primal Ockham algebras, and the other family is a sequence of generalised Stone algebras.