English

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

Rings and Algebras 2025-08-12 v1 Logic in Computer Science

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.

Keywords

Cite

@article{arxiv.2508.06918,
  title  = {Mal'cev clones over a three-element set up to minor-equivalence},
  author = {Stefano Fioravanti and Michael Kompatscher and Bernardo Rossi and Albert Vucaj},
  journal= {arXiv preprint arXiv:2508.06918},
  year   = {2025}
}

Comments

33 pages, 4 figures; appendix contains a github link with additional material