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https://open.uns.ac.rs/handle/123456789/20699
Title: | Posets of Copies of Countable Non-Scattered Labeled Linear Orders | Authors: | Kurilić Miloš Todorčević Stevo |
Issue Date: | 2020 | Journal: | Order: A Journal on the Theory of Ordered Sets and its Applications | Abstract: | © 2019, Springer Nature B.V. We show that the poset of copies ℙ(ℚn) = 〈 { f[X] : f∈ Emb (ℚn) } , ⊂ 〉 of the countable homogeneous universal n-labeled linear order, ℚn, is forcing equivalent to the poset S∗ π, where S is the Sacks perfect set forcing and 1 S⊢ “π is an atomless separative σ-closed forcing”. Under CH (or under some weaker assumptions) 1 S⊢ “π is forcing equivalent to P(ω)/Fin”. In addition, these statements hold for each countable non-scattered n-labeled linear order L and we have rosq ℙ(L) ≅ rosq ℙ(ℚn) ≅ rosq (S∗ π). | URI: | https://open.uns.ac.rs/handle/123456789/20699 | ISSN: | 0167-8094 | DOI: | 10.1007/s11083-019-09492-5 |
Appears in Collections: | PMF Publikacije/Publications |
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