Congruence Lattices of Semilattices with Operators

Abstract. The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have Con(S, +, 0, G) ∼=d Sp(L, H), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices satisfy the J´onsson-Kiefer property.

• Type: Journal
• Year: 2016
• Where: SLOGICA
• Authors: Jennifer Hyndman, James B. Nation, Joy Nishida
• Keywords: SLOGICA 2016, Software Engineering