Remarks on generalized ultrafilter, dominating and reaping numbers

Shimon Garti, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The following statements are the main results of the paper: (a) cf(u) > ω and cf(uκ) > ω for every uncountable cardinal κ where uκ is the generalized ultrafilter number. (b) If κ > ℵ0 is regular and rκ < dκ then rκ = uκ, where rκ is the generalized reaping number and dκ is the generalized dominating number. (c) The relations rλ < dλ and uλ < dλ are consistent for a strong limit singular cardinal λ.

Original languageAmerican English
Pages (from-to)101-115
Number of pages15
JournalFundamenta Mathematicae
Volume250
Issue number2
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2020

Keywords

  • Pcf theory. Received 25 June 2018; revised 22 January 2019
  • Reaping and dominating numbers
  • Ultrafilter number

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