Sublattice subgroups of finitely presented lattice-ordered groups

Graham Higman proved that the finitely generated groups that occur as subgroups of finitely presented groups are precisely those that can be defined by recursively enumerable sets of relations. We prove the analogue for lattice-ordered groups: Theorem A finitely generated lattice-ordered group is a sublattice subgroup of some finitely presented lattice-ordered group if and only if it can be defined by a recursively enumerable set of relations. Consequently, there is a universal finitely presented lattice-ordered group.