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

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
Externally published	Yes

Bibliographical note

Funding Information:
✩ The authors were partially supported by: The Austrian “Fonds zur wissenschaftlichen Förderung”, Grant No. 16334 and the University of Helsinki (first author), the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation, Germany (first and third author), the United States–Israel Binational Science Foundation Grant No. 2002323 (second author), the Golda Meir Fund and the Koshland Fellowship (third author). This is the second author’s publication 858. * Corresponding author. E-mail addresses: [email protected] (H. Mildenberger), [email protected] (S. Shelah), [email protected] (B. Tsaban). URL: http://www.cs.biu.ac.il/~tsaban.

Funding

✩ The authors were partially supported by: The Austrian “Fonds zur wissenschaftlichen Förderung”, Grant No. 16334 and the University of Helsinki (first author), the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation, Germany (first and third author), the United States–Israel Binational Science Foundation Grant No. 2002323 (second author), the Golda Meir Fund and the Koshland Fellowship (third author). This is the second author’s publication 858. * Corresponding author. E-mail addresses: [email protected] (H. Mildenberger), [email protected] (S. Shelah), [email protected] (B. Tsaban). URL: http://www.cs.biu.ac.il/~tsaban.

Funders	Funder number
Golda Meir Fund
Helsingin Yliopisto
Minerva Foundation
United States-Israel Binational Science Foundation	2002323
Holcim Stiftung zur Förderung der Wissenschaftlichen Fortbildung	16334

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

Cite this

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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.",

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

author = "Heike Mildenberger and Saharon Shelah and Boaz Tsaban",

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KW - Selection principles

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KW - ω-cover

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The combinatorics of τ-covers

Abstract

Bibliographical note

Funding

Keywords

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