In mathematics, a join-semilattice is a partially ordered set that has a join for any nonempty finite subset. Wikipedia

A partially ordered set in which every nonempty finite set has a least upper bound or in which every nonempty finite set has a greatest lower bound Wikidata

A partially ordered set that either has a join (a least upper bound) for any nonempty finite subset (a join-semilattice or upper semilattice) or has a meet (or greatest lower bound) for any nonempty finite subset (a meet-semilattice or lower semilattice). Wiktionary