2013•arXiv (Cornell University)Open access

Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous\n Partial Orders

Miloš S. Kurilić, Boriša Kuzeljević

Abstract

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

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Key concepts: Antichain, Partially ordered set, Mathematics, Countable set, Combinatorics, Nowhere dense set, Order (exchange), Order type