structural:scholar_edition
Free lattices

Any set X {\displaystyle X} may be used to generate the free semilattice F X. {\displaystyle FX.} The free semilattice is defined to consist of all of the finite subsets of X, {\displaystyle X,} with the semilattice operation given by ordinary set union. The free semilattice has the universal property. For the free lattice over a set X, {\displaystyle X,} Whitman gave a construction based on polynomials over X {\displaystyle X} ' s members.