Many different uniformity numbers of Yorioka ideals

Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardin...

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Bibliographic Details
Published in:Archive for mathematical logic 2022-07, Vol.61 (5-6), p.653-683
Main Authors: Klausner, Lukas Daniel, Mejía, Diego Alejandro
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Set theory
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Summary:Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals’ uniformity numbers can be pairwise different. In addition we show that, in the same forcing extension, for two other types of simple cardinal characteristics parametrised by reals (localisation and anti-localisation cardinals), for uncountably many parameters the corresponding cardinals are pairwise different.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-021-00809-z