Journal
ARCHIVE FOR MATHEMATICAL LOGIC
Volume 62, Issue 7-8, Pages 965-990Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00153-023-00881-7
Keywords
Descriptive set theory; Cardinal invariants; Regularity properties of the real line; Forcing
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This paper introduces and investigates versions of Silver and Mathias forcing with respect to lower and upper density. The focus is on properness, Axiom A, chain conditions, preservation of cardinals, and adding Cohen reals. We discover rough forcings that collapse 2ᶿ to ᶿ, while others are surprisingly gentle. We also study the connections between regularity properties induced by these parametrized forcing notions and the Baire property.
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? to ?, while others are surprisingly gentle. We also study connections between regularity properties induced by these parametrized forcing notions and the Baire property.
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