Embedding finitely generated Abelian lattice-ordered groups : Higman's theorem and a realisation of \pi

Graham Higman proved that a finitely generated group can be embedded in a finitely presented group if and only if it has a recursively enumerable set of defining relations. The analogue for lattice-ordered groups is considered here. Clearly, the finitely generated lattice-ordered groups that can be embedded in finitely presented lattice-ordered groups must have recursively enumerable sets of defining relations. The converse direction is proved for a special class of lattice-ordered groups.