ON THE (UN)DECIDABILITY OF A NU-TERM

We investigate two problems: the natural duality problem (given a finite algebra P, decide if the quasi-variety generated by P is dualizable) and the near-unanimity problem (given a finite algebra, decide if it has a near-unanimity term of finite arity). These problems are intimately related to each other as described in [2]. We prove that a partial version of the second problem is undecidable. On the other hand, we present results towards proving the decidability of the general problem.