Displaying similar documents to “Small sets with respect to certain classes of topologies”

A dichotomy for P-ideals of countable sets

Stevo Todorčević (2000)

Fundamenta Mathematicae

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A dichotomy concerning ideals of countable subsets of some set is introduced and proved compatible with the Continuum Hypothesis. The dichotomy has influence not only on the Suslin Hypothesis or the structure of Hausdorff gaps in the quotient algebra P ( ℕ ) / but also on some higher order statements like for example the existence of Jensen square sequences.

On the ideal (v 0)

Piotr Kalemba, Szymon Plewik, Anna Wojciechowska (2008)

Open Mathematics

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The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0)...

The covering property for σ-ideals of compact, sets

Carlos Uzcátegui (1992)

Fundamenta Mathematicae

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The covering property for σ-ideals of compact sets is an abstract version of the classical perfect set theorem for analytic sets. We will study its consequences using as a paradigm the σ-ideal of countable closed subsets of 2 ω .