  We study the degree spectra and reverse-mathematical applications of
computably enumerable and co-computably enumerable partial orders. We formulate
versions of the chain/antichain principle and ascending/descending sequence
principle for such orders, and show that the former is strictly stronger than
the latter. We then show that every $\emptyset'$-computable structure (or even
just of c.e.\ degree) has the same degree spectrum as some computably
enumerable (co-c.e.)\ partial order, and hence that there is a c.e.\ (co-c.e.)\
partial order with spectrum equal to the set of nonzero degrees.
