Displaying similar documents to “Perfect sets and collapsing continuum”

On π -caliber and an application of Prikry’s partial order

Andrzej Szymański (2011)

Commentationes Mathematicae Universitatis Carolinae

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We study the concept of π -caliber as an alternative to the well known concept of caliber. π -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, π -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, 2 ω is a π -caliber of ℕ * . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.

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...

Cardinal inequalities implying maximal resolvability

Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta (2005)

Commentationes Mathematicae Universitatis Carolinae

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We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space X is maximally resolvable provided that for a dense set X 0 ⊂ X and for each x ∈ X 0 the π -character of X at x is not greater than the dispersion character of X . On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.

Strong remote points

Sergei Logunov (2002)

Commentationes Mathematicae Universitatis Carolinae

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Remote points constructed so far are actually strong remote. But we construct remote points of another type.