Abstract
In [1] Baldwin and Berman ask if a variety generated by a finite algebra 91 has definable principal congruences, i.e. is there a first-order formula ~(x, y, u, v) such that for any ~eo//.(91) and a , b , c , d in 2~ we have (c, d>~O(a,b) iff ~cI)(a, b, c, d). In the following we describe a four-element algebra 91 such that ~ has distributive congruence lattices and does not have definable principal congruences. Let 91 =<A, + , t} where A ={0, 1, 2, 3} and the operations are given by
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