In mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset...

arrangement of planes. The intersection semilattice L(A) is a meet semilattice and more specifically is a geometric semilattice. If the arrangement is linear or...

pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that...

theorem for commutative semigroups in terms of semilattices. A semilattice (or more precisely a meet-semilattice) (L, ≤) is a partially ordered set where every...

equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras...

called a closed sublattice of L. The terms complete meet-semilattice or complete join-semilattice are another way to refer to complete lattices since arbitrary...

least lattices, but the concept can in fact reasonably be generalized to semilattices as well. Probably the most common type of distributivity is the one defined...

valuable alternative presentation. In the case of semilattices, an explicit construction of the free semilattice F ∨ ( X ) {\displaystyle F_{\vee }(X)} is straightforward...

generalized Boolean algebra, while (B, ∨, 0) is a generalized Boolean semilattice. Generalized Boolean lattices are exactly the ideals of Boolean lattices...

residuated Boolean algebras, relation algebras, and MV-algebras. Residuated semilattices omit the meet operation ∧, for example Kleene algebras and action algebras...