 Free Abelian lattice-ordered group

The free object on generators $x_1,\dots ,x_n$ has the universal property that an arbitrary assignment of these generators to an Abelian lattice-ordered group extends uniquely to a lattice-ordered group homomorphism. It can be constructed from terms using addition, negation, zero, join and meet, modulo identities valid in every Abelian lattice-ordered group. Its underlying group need not be finitely generated even when there are only two lattice generators.