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2017 Canjar Filters
Osvaldo Guzmán, Michael Hrušák, Arturo Martínez-Celis
Notre Dame J. Formal Logic 58(1): 79-95 (2017). DOI: 10.1215/00294527-3496040

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.

Citation

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Osvaldo Guzmán. Michael Hrušák. Arturo Martínez-Celis. "Canjar Filters." Notre Dame J. Formal Logic 58 (1) 79 - 95, 2017. https://doi.org/10.1215/00294527-3496040

Information

Received: 1 September 2012; Accepted: 14 October 2013; Published: 2017
First available in Project Euclid: 6 April 2016

zbMATH: 06686418
MathSciNet: MR3595342
Digital Object Identifier: 10.1215/00294527-3496040

Subjects:
Primary: 03E05
Secondary: 03E17, 03E35

Rights: Copyright © 2017 University of Notre Dame

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Vol.58 • No. 1 • 2017
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