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Title: MAD families and the rationals (English)
Author: Hrušák, Michael
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 42
Issue: 2
Year: 2001
Pages: 345-352
Category: math
Summary: Rational numbers are used to classify maximal almost disjoint (MAD) families of subsets of the integers. Combinatorial characterization of indestructibility of MAD families by the likes of Cohen, Miller and Sacks forcings are presented. Using these it is shown that Sacks indestructible MAD family exists in ZFC and that $\frak b =\frak c$ implies that there is a Cohen indestructible MAD family. It follows that a Cohen indestructible MAD family is in fact indestructible by Sacks and Miller forcings. A connection with Roitman's problem of whether $\frak d=\omega_1$ implies $\frak a=\omega_1$ is also discussed. (English)
Keyword: maximal almost disjoint family; Cohen
Keyword: Miller
Keyword: Sacks forcing; cardinal invariants of the continuum
MSC: 03E05
MSC: 03E17
MSC: 03E20
idZBL: Zbl 1051.03039
idMR: MR1832152
Date available: 2009-01-08T19:10:29Z
Last updated: 2012-04-30
Stable URL:
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