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Making doughnuts of Cohen reals
Author(s) -
Halbeisen Lorenz
Publication year - 2003
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310016
Subject(s) - property (philosophy) , mathematics , disjoint sets , forcing (mathematics) , set (abstract data type) , combinatorics , discrete mathematics , computer science , mathematical analysis , philosophy , epistemology , programming language
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 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 ℬ or the Ramsey property ℛ. In this paper it is shown that a finite support iteration of length ω 1 of Cohen forcing, starting from L , yields a model for CH + $ \sum ^1 _2 $ () + $ \neg \sum ^1 _2 $ (ℬ) + $ \neg \sum ^1 _2 $ (ℛ).