Undecidable varieties with solvable word problems. II.
An algebra is uniform if for each , every two classes of have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
2000 Mathematics Subject Classification: 06A06, 54E15An ordered pair X(R) = ( X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, apparently quite different, types of notions are closely...
We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.