Towers, mad families, and unboundedness

Vera Fischer; Wolfgang Wohofsky; Marlene Elisabeth Koelbing

doi:10.1007/s00153-023-00861-x

Towers, mad families, and unboundedness

Vera Fischer, Wolfgang Wohofsky, Marlene Elisabeth Koelbing

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are B-Canjar for any countably directed unbounded family B of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that b=ω1 in every extension by the above forcing notions.

Original language	English
Pages (from-to)	811-830
Number of pages	20
Journal	Archive for Mathematical Logic
Volume	62
Issue number	5-6
Early online date	12 Feb 2023
DOIs	https://doi.org/10.1007/s00153-023-00861-x
Publication status	Published - Jul 2023

Austrian Fields of Science 2012

101013 Mathematical logic

Keywords

Canjar filters
Forcing
Maximal almost disjoint families
Towers
Unboundedness

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10.1007/s00153-023-00861-xLicence: CC BY 4.0

https://phaidra.univie.ac.at/o:1952631Licence: CC BY 4.0

Cite this

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KW - Maximal almost disjoint families

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KW - Unboundedness

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Towers, mad families, and unboundedness

Abstract

Austrian Fields of Science 2012

Keywords

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