Title
HIGHER INDEPENDENCE
Author
Abstract
We study higher analogues of the classical independence number on ω . For κ regular uncountable, we denote by i(κ) the minimal size of a maximal κ -independent family. We establish ZFC relations between i(κ) and the standard higher analogues of some of the classical cardinal characteristics, e.g., r(κ)≤i(κ) and d(κ)≤i(κ) . For κ measurable, assuming that 2κ=κ+ we construct a maximal κ -independent family which remains maximal after the κ -support product of λ many copies of κ -Sacks forcing. Thus, we show the consistency of κ+=d(κ)=i(κ)<2κ . We conclude the paper with interesting open questions and discuss difficulties regarding other natural approaches to higher independence.
Keywords
cardinal characteristicsindependent familiesgeneralised Baire spaceslarge cardinalsforcing
Object type
Language
English [eng]
Persistent identifier
Appeared in
Title
The Journal of Symbolic Logic
Volume
87
Issue
4
ISSN
0022-4812
Issued
2022
From page
1606
To page
1630
Publication
Cambridge University Press (CUP)
Version type
Date issued
2022
Access rights
Rights
Rights statement
© The Author(s), 2022
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