Finitely presented partially ordered abelian groups

We study the partially-ordered abelian group, F (P; R), generated by a set of generators,P , and inequality relations, R, and its representations in Euclidean space. First F (P; R) is deened by a universal property and then existence is shown proof-theoretically. We then characterize the order structure of F (P; R). The rst main result of the paper utilizes the Marriage Theorem to prove that if the set of relations , R, is derived from a nite partially-ordered set then F (P; R) is isomorphically embeddable in R n for n suuciently large. The second main result utilizes the Compactness Theorem to prove that for nite R, F (P; R) is pseudo-Archimedean.