Maximal Chains of Isomorphic Subgraphs of Countable Ultrahomogeneous Graphs
نویسندگان
چکیده
For a countable ultrahomogeneous graph G = 〈G, ρ〉 let P(G) denote the collection of sets A ⊂ G such that 〈A, ρ ∩ [A]〉 ∼= G. The order types of maximal chains in the poset 〈P(G) ∪ {∅},⊂〉 are characterized as: (I) the order types of compact sets of reals having the minimum nonisolated, if G is the Rado graph or the Henson graph Hn, for some n ≥ 3; (II) the order types of compact nowhere dense sets of reals having the minimum non-isolated, if G is the union of μ disjoint complete graphs of size ν, where μν = ω. 2010 MSC: 05C63, 05C80, 05C60, 06A05, 06A06, 03C50, 03C15.
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