, Volume 57, Issue 2, pp 215-237
Date: 18 Sep 2007

On the (un)decidability of a near-unanimity term

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Abstract.

We investigate the near-unanimity problem: given a finite algebra, decide if it has a near-unanimity term of finite arity. We prove that it is undecidable of a finite algebra if it has a partial near-unanimity term on its underlying set excluding two fixed elements. On the other hand, based on Rosenberg’s characterization of maximal clones, we present partial results towards proving the decidability of the general problem.

Presented by K. Kearnes.
Received February 21, 2005; accepted in final form November 25, 2006.
While working on this paper, the author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant nos. T 37877 and K 60148.