Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders

Abstract

© 2014, Springer Science+Business Media Dordrecht. We investigate the poset 〈ℙ(𝕏) ∪ {∅}, ⊂〉, where 𝕏 is a countable ultrahomogeneous partial order and ℙ(𝕏) the set of suborders of 𝕏 isomorphic to 𝕏. For 𝕏 different from (resp. equal to) a countable antichain the order types of maximal chains in 〈ℙ(𝕏) ∪ {∅}, ⊂〉 are characterized as the order types of compact (resp. compact and nowhere dense) sets ofreals having the minimum non-isolated.