Covering the Baire space by families which are not finitely dominating

Heike Mildenberger; Saharon Shelah; Boaz Tsaban

doi:10.1016/j.apal.2005.09.008

Covering the Baire space by families which are not finitely dominating

Heike Mildenberger, Saharon Shelah, Boaz Tsaban

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

8 Scopus citations

Abstract

It is consistent (relative to ZFC) that each union of max {b,g} many families in the Baire space ω_ω which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower ω_ω/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.

Original language	English
Pages (from-to)	60-71
Number of pages	12
Journal	Annals of Pure and Applied Logic
Volume	140
Issue number	1-3
DOIs	https://doi.org/10.1016/j.apal.2005.09.008
State	Published - Jul 2006
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 authors), the United States–Israel Binational Science Foundation Grant no. 2002323 (second author), and the Golda Meir Fund (third author). This is the second author’s publication 847.

Keywords

Cofinality of ultrapowers
Finitely dominating families
Groupwise density number g
Unbounding number b

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10.1016/j.apal.2005.09.008

Cite this

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abstract = "It is consistent (relative to ZFC) that each union of max {b,g} many families in the Baire space ωω which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower ωω/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.",

keywords = "Cofinality of ultrapowers, Finitely dominating families, Groupwise density number g, Unbounding number b",

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

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KW - Unbounding number b

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Covering the Baire space by families which are not finitely dominating

Abstract

Bibliographical note

Keywords

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