A version of κ-Miller forcing

We consider a version of κ -Miller forcing on an uncountable cardinal κ . We show that under 2 < κ = κ this forcing collapses 2 κ to ω and adds a κ -Cohen real. The same holds under the weaker assumptions that cf ( κ ) > ω , 2 2 < κ = 2 κ , and forcing with ( [ κ ] κ , ⊆ ) collapses 2 κ to...

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Bibliographic Details
Published in:Archive for mathematical logic 2020-11, Vol.59 (7-8), p.879-892
Main Authors: Mildenberger, Heike, Shelah, Saharon
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
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Summary:We consider a version of κ -Miller forcing on an uncountable cardinal κ . We show that under 2 < κ = κ this forcing collapses 2 κ to ω and adds a κ -Cohen real. The same holds under the weaker assumptions that cf ( κ ) > ω , 2 2 < κ = 2 κ , and forcing with ( [ κ ] κ , ⊆ ) collapses 2 κ to ω .
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-020-00721-y