Mal'cev clones over a three-element set up to minor-equivalence

TL;DR

This paper classifies all Mal'cev clones over a three-element set up to minor-equivalence, advancing the understanding of three-element relational structures and providing an alternative proof regarding their relational bases.

Contribution

It offers a complete classification of Mal'cev clones over a three-element set up to minor-equivalence and presents an alternative proof of their relational basis size.

Findings

All Mal'cev clones over a three-element set are classified up to minion homomorphisms.

Proved that these clones have an at most 4-ary relational basis.

Contributes to the broader goal of classifying three-element relational structures.

Abstract

We classify all Mal'cev clones over a three-element set up to minion homomorphisms. This is another step toward the complete classification of three-element relational structures up to pp-constructability. We furthermore provide an alternative proof of Bulatov's result that all Mal'cev clones over a three-element set have an at most 4-ary relational basis.