The combinatorics of τ-covers

Heike Mildenberger; Saharon Shelah; Boaz Tsaban

doi:10.1016/j.topol.2006.04.011

The combinatorics of τ-covers

Heike Mildenberger
, Saharon Shelah
, Boaz Tsaban^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We solve four out of the six open problems concerning critical cardinalities of topological diagonalization properties involving τ-covers, show that the remaining two cardinals are equal, and give a consistency result concerning this remaining cardinal. Consequently, 21 open problems concerning potential implications between these properties are settled. We also give structural results based on the combinatorial techniques.

Original language	English
Pages (from-to)	263-276
Number of pages	14
Journal	Topology and its Applications
Volume	154
Issue number	1
DOIs	https://doi.org/10.1016/j.topol.2006.04.011
State	Published - 1 Jan 2007

Keywords

Borel covers
Combinatorial cardinal characteristics of the continuum
Open covers
Selection principles
γ-cover
τ-cover
ω-cover

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10.1016/j.topol.2006.04.011

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AB - We solve four out of the six open problems concerning critical cardinalities of topological diagonalization properties involving τ-covers, show that the remaining two cardinals are equal, and give a consistency result concerning this remaining cardinal. Consequently, 21 open problems concerning potential implications between these properties are settled. We also give structural results based on the combinatorial techniques.

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KW - Combinatorial cardinal characteristics of the continuum

KW - Open covers

KW - Selection principles

KW - γ-cover

KW - τ-cover

KW - ω-cover

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The combinatorics of τ-covers

Abstract

Keywords

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