Finite atomistic lattices that can be represented as lattices of quasivarieties
Volume 142 / 1993
Fundamenta Mathematicae 142 (1993), 19-43 DOI: 10.4064/fm-142-1-19-43
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of .