Ultrafilters on w-their ideals and their cardinal characteristics

Jörg Brendle; Saharon Shelah

doi:10.1090/s0002-9947-99-02257-6

Ultrafilters on w-their ideals and their cardinal characteristics

Jörg Brendle^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

31 Scopus citations

Abstract

For a free ultrafilter μ on ω we study several cardinal characteristics which describe part of the combinatorial structure of μ. We provide various consistency results; e.g. we show how to force simultaneously many characters and many π-characters. We also investigate two ideals on the Baire space ω^ω naturally related to μ and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.

Original language	English
Pages (from-to)	2643-2674
Number of pages	32
Journal	Transactions of the American Mathematical Society
Volume	351
Issue number	7
DOIs	https://doi.org/10.1090/s0002-9947-99-02257-6
State	Published - 1999

Keywords

Cardinal coefficient
Character
Easton forcing
Ideal
Laver forcing
Mathias forcing
P-point
Ramsey null sets (nowhere ramsey sets)
Ramsey ultrafilter
Tr-character
Ultrafilter

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10.1090/s0002-9947-99-02257-6

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KW - Character

KW - Easton forcing

KW - Ideal

KW - Laver forcing

KW - Mathias forcing

KW - P-point

KW - Ramsey null sets (nowhere ramsey sets)

KW - Ramsey ultrafilter

KW - Tr-character

KW - Ultrafilter

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Ultrafilters on w-their ideals and their cardinal characteristics

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Keywords

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