Mathias and silver forcing parametrized by density

We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2 ω to ω , while others are surprisingly gentle. We also...

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Bibliographic Details
Published in:Archive for mathematical logic 2023-11, Vol.62 (7-8), p.965-990
Main Authors: Laguzzi, Giorgio, Mildenberger, Heike, Stuber-Rousselle, Brendan
Format: Article
Language:English
Subjects:
Algebra
Density
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Parameterization
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Summary:We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardinals and adding Cohen reals. We find rough forcings that collapse 2 ω to ω , while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-023-00881-7