The ultrafilter number for singular cardinals

Shimon Garti; Saharon Shelah

doi:10.1007/s10474-012-0245-0

The ultrafilter number for singular cardinals

Shimon Garti^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

13 Scopus citations

Abstract

We prove the consistency of a singular cardinal λ with small value of the ultrafilter number u _λ, and arbitrarily large value of 2 ^λ.

Original language	English
Pages (from-to)	296-301
Number of pages	6
Journal	Acta Mathematica Hungarica
Volume	137
Issue number	4
DOIs	https://doi.org/10.1007/s10474-012-0245-0
State	Published - Nov 2012

Bibliographical note

Funding Information:
∗Corresponding author. †Research supported by the United States-Israel Binational Science Foundation, and ISF grant no. 242/03. This is publication 1002 of the second author. Key words and phrases: ultrafilter number, pcf theory, large cardinal. Mathematics Subject Classification: 03E05, 03E55.

Keywords

large cardinal
pcf theory
ultrafilter number

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10.1007/s10474-012-0245-0

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title = "The ultrafilter number for singular cardinals",

abstract = "We prove the consistency of a singular cardinal λ with small value of the ultrafilter number u λ, and arbitrarily large value of 2 λ.",

keywords = "large cardinal, pcf theory, ultrafilter number",

author = "Shimon Garti and Saharon Shelah",

note = "Funding Information: ∗Corresponding author. †Research supported by the United States-Israel Binational Science Foundation, and ISF grant no. 242/03. This is publication 1002 of the second author. Key words and phrases: ultrafilter number, pcf theory, large cardinal. Mathematics Subject Classification: 03E05, 03E55.",

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AU - Shelah, Saharon

N1 - Funding Information: ∗Corresponding author. †Research supported by the United States-Israel Binational Science Foundation, and ISF grant no. 242/03. This is publication 1002 of the second author. Key words and phrases: ultrafilter number, pcf theory, large cardinal. Mathematics Subject Classification: 03E05, 03E55.

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N2 - We prove the consistency of a singular cardinal λ with small value of the ultrafilter number u λ, and arbitrarily large value of 2 λ.

AB - We prove the consistency of a singular cardinal λ with small value of the ultrafilter number u λ, and arbitrarily large value of 2 λ.

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KW - pcf theory

KW - ultrafilter number

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The ultrafilter number for singular cardinals

Abstract

Bibliographical note

Keywords

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