Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders

We investigate the poset (P(X),\subset), where P(X) is the set of isomorphic suborders of a countable ultrahomogeneous partial order X. For X different from (resp. equal to) a countable antichain the order types of maximal chains in (P(X)\cup {\emptyset },\subset) are characterized as the order types of compact (resp. compact and nowhere dense) sets of reals having the minimum non-isolated.