  We study notions such as &#64257;nite presentability and coherence, for
partially ordered abelian groups and vector spaces. Typical results are the
following: (i) A partially ordered abelian group G is &#64257;nitely presented
if and only if G is &#64257;nitely generated as a group, the positive cone G^+
is well-founded as a partially ordered set, and the set of minimal elements of
(G^+)-{0} is &#64257;nite. (ii) Torsion-free, &#64257;nitely presented
partially ordered abelian groups can be represented as subgroups of some Z^n,
with a &#64257;nitely generated submonoid of (Z+)^n as positive cone. (iii)
Every unperforated, &#64257;nitely presented partially ordered abelian group is
Archimedean. Further, we establish connections with interpolation. In
particular, we prove that a divisible dimension group G is a directed union of
simplicial subgroups if and only if every &#64257;nite subset of G is contained
into a &#64257;nitely presented ordered subgroup.
