Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 58, Number 1 (2017), 79-95.
If is a filter on , we say that is Canjar if the corresponding Mathias forcing does not add a dominating real. We prove that any Borel Canjar filter is , solving a problem of Hrušák and Minami. We give several examples of Canjar and non-Canjar filters; in particular, we construct a 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 there are 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 on subsets of the Cantor space.
Notre Dame J. Formal Logic, Volume 58, Number 1 (2017), 79-95.
Received: 1 September 2012
Accepted: 14 October 2013
First available in Project Euclid: 6 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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