Displaying similar documents to “Almost disjoint families and “never” cardinal invariants”

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 .

Property ( a ) and dominating families

Samuel Gomes da Silva (2005)

Commentationes Mathematicae Universitatis Carolinae

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Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal...

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). ...

Special almost P-spaces

Alessandro Fedeli (1997)

Commentationes Mathematicae Universitatis Carolinae

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Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space X of this kind the inequality “ | X | ≤ ψ c ( X ) t ( X ) " holds.