Displaying similar documents to “Forcing indestructible extensions of almost disjoint families”

MAD families and the rationals

Michael Hrušák (2001)

Commentationes Mathematicae Universitatis Carolinae

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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 𝔟 = 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...

Around splitting and reaping

Jörg Brendle (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number 𝔰 or its dual, the reaping number 𝔯 .