On the ideal (v 0)

• Autorzy: Piotr Kalemba , Szymon Plewik , Anna Wojciechowska
• Języki publikacji: EN

Abstrakty

EN

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) has the ideal type (c, ω 1, c).

Słowa kluczowe

EN

base v-matrix; doughnut; ideal type; ideal (v 0)

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 03E35: Consistency and independence results
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 218-227

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Piotr Kalemba

• University of Silesia

autor

Szymon Plewik

• University of Silesia

autor

Anna Wojciechowska

• University of Silesia

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Identyfikatory

DOI

10.2478/s11533-008-0021-0