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Making doughnuts of Cohen reals.
- Source :
-
Mathematical Logic Quarterly . Mar2003, Vol. 49 Issue 2, p173-178. 6p. - Publication Year :
- 2003
-
Abstract
- For a ⊆ b ⊆ ω with b\ a infinite, the set D = {x ∈ [ω]ω : a ⊆ x ⊆ b} is called a doughnut. A set S ⊆ [ω]ω has the doughnut property &Dscr; if it contains or is disjoint from a doughnut. It is known that not every set S ⊆ [ω]ω has the doughnut property, but S has the doughnut property if it has the Baire property &Bscr; or the Ramsey property ℛ. In this paper it is shown that a finite support iteration of length ω1 of Cohen forcing, starting from <BI>L</BI>, yields a model for CH + <UEQN>$ \sum ^1 _2 $</UEQN>(&Dscr;) + <UEQN>$ \neg \sum ^1 _2 $</UEQN>(&Bscr;) + <UEQN>$ \neg \sum ^1 _2 $</UEQN>(ℛ). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09425616
- Volume :
- 49
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematical Logic Quarterly
- Publication Type :
- Academic Journal
- Accession number :
- 13643760
- Full Text :
- https://doi.org/10.1002/malq.200310016