Inflation of Finite Lattices Along All-or-nothing Sets

摘要

We introduce a new generalization of Alan Day's doubling construction. For ordered sets and and a subset we define the ordered set arising from inflation of along E by . Under the restriction that and are finite lattices, we find those subsets such that the ordered set is a lattice. Finite lattices that can be constructed in this way are classified in terms of their congruence lattices.