Authors: Kurilić, Miloš
Todorčević, Stevo 
Title: Forcing by non-scattered sets
Journal: Annals of Pure and Applied Logic
Volume: 163
Issue: 9
First page: 1299
Last page: 1308
Issue Date: 1-Sep-2012
Rank: M22
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.02.004
Abstract: 
We show that for each non-scattered linear order 〈 L, < 〉 the set of non-scattered subsets of L ordered by the inclusion is forcing equivalent to the two-step iteration of the Sacks forcing and a σ-closed forcing. If the equality sh(S)=א1 or PFA holds in the ground model, then the second iterand is forcing equivalent to the algebra P(ω) / Fin of the Sacks extension.
Keywords: σ-closed forcing | Ideal | Linear order | Non-scattered set | Sacks forcing
Publisher: Elsevier
Project: Set Theory, Model Theory and Set-Theoretic Topology 

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