Displaying similar documents to “Strongly discrete subsets in ω*”

Almost disjoint families and property (a)

Paul Szeptycki, Jerry Vaughan (1998)

Fundamenta Mathematicae

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We consider the question: when does a Ψ-space satisfy property (a)? We show that if | A | < p then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality p which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a). ...

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...