Remarks on the Fraser-Horn property
A variety of algebras has the Fraser-Horn property (FHP) if all congruences of a direct product of two algebras are product congruences. A variety has definable principal congruences (DPC) if there exists a first order four-ary formula which describes the principal congruences. If this formula can be given as a (finite) set of equations, the variety has equationally definable principal congruences (EDPC). The important result of this short paper is that in any variety: \(EDPC=DPC+FHP\).
equationally definable principal congruences
scientific article; zbMATH DE number 3977071