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

^*Corresponding author for this work

Einstein Institute of Mathematics

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

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

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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.",

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KW - Cofinality of ultrapowers

KW - Finitely dominating families

KW - Groupwise density number g

KW - Unbounding number b

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ER -

Covering the Baire space by families which are not finitely dominating

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Keywords

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