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The existence of a near-unanimity term in a finite algebra is decidable. (English) Zbl 1174.08002
Near-unanimity operations are characterized by the identities \[ f(y,x,\dots,x) = f(x,y,x,\dots,x) = \dots = f(x,\dots,x,y) = x. \] B. A. Davey, L. Heindorf, and R. McKenzie [Algebra Univers. 33, No. 3, 428–439 (1995; Zbl 0824.08007)] posed the problem whether having a near-unanimity term operation is a decidable property of finite algebras. From the affirmative solution elaborated in the present paper also follows the decidability of the natural duality problem for finite algebras in congruence distributive varieties.

MSC:
08A40 Operations and polynomials in algebraic structures, primal algebras
08B10 Congruence modularity, congruence distributivity
03B25 Decidability of theories and sets of sentences
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