Notre Dame Journal of Formal Logic

Canjar Filters

Osvaldo Guzmán, Michael Hrušák, and Arturo Martínez-Celis

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Abstract

If F is a filter on ω, we say that F is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is Fσ, solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a MAD family such that the corresponding Mathias forcing adds a dominating real. This answers a question of Brendle. Then we prove that in all the “classical” models of ZFC there are MAD families whose Mathias forcing does not add a dominating real. We also study ideals generated by branches, and we uncover a close relation between Canjar ideals and the selection principle Sfin(Ω,Ω) on subsets of the Cantor space.

Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 1 (2017), 79-95.

Dates
Received: 1 September 2012
Accepted: 14 October 2013
First available in Project Euclid: 6 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1459967875

Digital Object Identifier
doi:10.1215/00294527-3496040

Mathematical Reviews number (MathSciNet)
MR3595342

Zentralblatt MATH identifier
06686418

Subjects
Primary: 03E05: Other combinatorial set theory
Secondary: 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results

Keywords
Canjar filters Mathias forcing dominating reals MAD families

Citation

Guzmán, Osvaldo; Hrušák, Michael; Martínez-Celis, Arturo. Canjar Filters. Notre Dame J. Formal Logic 58 (2017), no. 1, 79--95. doi:10.1215/00294527-3496040. https://projecteuclid.org/euclid.ndjfl/1459967875


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