We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R for some finitary relation R over A. It follows that for a fixed finite set A, the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra with few subpowers has a finitely related clone of term operations. Hence modulo term equivalence and a renaming of the elements, there are only countably many finite algebras with few subpowers, and thus only countably many finite algebras with a Malcev term.
Sprache der Kurzfassung:
Englisch
Journal:
arXiv.org
Number:
arXiv:1103.2265
Erscheinungsmonat:
5
Erscheinungsjahr:
2011
ISSN:
2331-8422
Anzahl der Seiten:
14
Reichweite:
international
Publikationstyp:
Aufsatz / Paper in Online-Archiv (nicht-referiert)
Forschungs-