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

The Hebrew University of Jerusalem

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

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 - 1 Jan 2020

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.4064/fm595-9-2019

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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.",

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AU - Shelah, Saharon

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Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Pcf theory. Received 25 June 2018; revised 22 January 2019

KW - Reaping and dominating numbers

KW - Ultrafilter number

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DO - 10.4064/fm595-9-2019

M3 - مقالة

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EP - 115

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 2

ER -

Remarks on generalized ultrafilter, dominating and reaping numbers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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