Mathias and silver forcing parametrized by density

Giorgio Laguzzi; Heike Mildenberger; Brendan Stuber-Rousselle

doi:10.1007/s00153-023-00881-7

Mathias and silver forcing parametrized by density

Giorgio Laguzzi
, Heike Mildenberger
, Brendan Stuber-Rousselle

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	965-990
Number of pages	26
Journal	Archive for Mathematical Logic
Volume	62
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-023-00881-7
Publication status	Published - Nov 2023
Externally published	Yes

Keywords

Cardinal invariants
Descriptive set theory
Forcing
Regularity properties of the real line

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10.1007/s00153-023-00881-7

Cite this

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abstract = "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.",

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AB - 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.

KW - Cardinal invariants

KW - Descriptive set theory

KW - Forcing

KW - Regularity properties of the real line

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Mathias and silver forcing parametrized by density

Abstract

Keywords

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