Displaying similar documents to “Combinatorial aspects of measure and category”

Measurable cardinals and category bases

Andrzej Szymański (1991)

Commentationes Mathematicae Universitatis Carolinae

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We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.

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)...