Covering the Baire space by families which are not finitely dominating

Heike Mildenberger, Saharon Shelah, Boaz Tsaban

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8 Scopus citations


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.

Original languageEnglish
Pages (from-to)60-71
Number of pages12
JournalAnnals of Pure and Applied Logic
Issue number1-3
StatePublished - Jul 2006
Externally publishedYes

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.


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


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