Congruences on Ockham algebras with pseudocomplementation

The variety pO consists of those algebras (L Lambda, V, f, *, 0, 1) where (L; Lambda, V, f, 0, 1) is an Ockham algebra, (L; Lambda, V, *, 0, 1) is a p-algebra, and the unary operations f and * commute. For an algebra in pK(omega) we show that the compact congruences Form a dual Stone lattice and use this to determine necessary and sufficient conditions for a principal congruence to be complemented. W also describe the lattice of subvarieties of pK(1,1), identifying therein the biggest subvariety in which every principal congruence is complemented, and the biggest subvariety in which the intersection of two principal congruences is principal.