Remarks on generalized ultrafilter, dominating and reaping numbers

Shimon Garti; Saharon Shelah

doi:10.4064/fm595-9-2019

Remarks on generalized ultrafilter, dominating and reaping numbers

Shimon Garti, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 r_λ < d_λ and u_λ < d_λ are consistent for a strong limit singular cardinal λ.

Original language	English
Pages (from-to)	101-115
Number of pages	15
Journal	Fundamenta Mathematicae
Volume	250
Issue number	2
DOIs	https://doi.org/10.4064/fm595-9-2019
State	Published - 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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10.4064/fm595-9-2019

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Remarks on generalized ultrafilter, dominating and reaping numbers

Abstract

Bibliographical note

Keywords

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