The lattice of convex subsemilattices of a semilattice
by
Peter R Jones
Marquette University (Milwaukee, Wisconsin)
Coauthors: Kyeong Hee Cheong (Korea)

Given a (meet-) semilattice E, the subsemilattices that are convex with respect to the order form a complete lattice, denoted LCV(E). While the question of how the lattice properties of LCV(E) affect E itself is of interest, we shall focus in this talk on the extent to which the lattice determines the semilattice: that is, given a semilattice E and semilattice F for which LCV(E) and LCV(F) are isomorphic, how is F related to E? Since any three-element semilattices have isomorphic such lattices, the answer is clearly not ``up to isomorphism''. It is perhaps surprising, then, that we are able to answer this question completely and to construct all such semilattices F from a given E.

There is a modest literature on the analogous question for the lattice of convex sublattices of a lattice.

Date received: December 26, 2001