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Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Novi Sad, Trg DositejaObradovića 4, 21000, Novi Sad, Serbia

    Miloš S. Kurilić

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001, Belgrade, Serbia

    Boriša Kuzeljević

Authors
  1. Miloš S. Kurilić
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  2. Boriša Kuzeljević
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Correspondence to Miloš S. Kurilić.

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S. Kurilić, M., Kuzeljević, B. Maximal Chains of Isomorphic Suborders of Countable Ultrahomogeneous Partial Orders. Order 32, 83–99 (2015). https://doi.org/10.1007/s11083-014-9317-9

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  • DOI: https://doi.org/10.1007/s11083-014-9317-9

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