Generalized independence

2023/02/17 by Hernández-Hernández, Fernando, López-Callejas, Carlos · 1 citation
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2302.09012

Abstract

We explore different generalizations of the classical concept of independent families on ω following the study initiated by Fisher and Montoya. We show that under \diamondsuit^*(κ) we can get strongly independent families on κ of size 2^κ and present an equivalence of GCH in terms of strongly independent families. We merge the two natural ways of generalizing independent families through a filter or an ideal and we focus on the C-independent families, where C is the club filter. Also we show a relationship between the existence of J-independent families and the saturation of the ideal J.

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• κ-barely independent families and Tukey types of ultrafilters

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• Filters and Ideal Independence
• Strong independence and its spectrum
• Higher Independence
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• Generic Existence of Independent Families