Authors: Kurilić, Miloš
Todorčević, Stevo 
Title: Posets of Copies of Countable Non-Scattered Labeled Linear Orders
Journal: Order : A Journal on the Theory of Ordered Sets and its Applications
Volume: 37
First page: 59
Last page: 72
Issue Date: 1-Jan-2019
Rank: M23
ISSN: 0167-8094
DOI: 10.1007/s11083-019-09492-5
Abstract: 
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).
Keywords: Countable homogeneous universal n-labeled linear order | Sacks forcing | σ-closed forcing
Publisher: Springer Link
Project: Set Theory, Model Theory and Set-Theoretic Topology 

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