The spectrum of independence

Vera Fischer*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study the set of possible sizes of maximal independent families to which we refer as spectrum of independence and denote Spec (mif). Here mif abbreviates maximal independent family. We show that:1.whenever κ1< ⋯ < κn are finitely many regular uncountable cardinals, it is consistent that {κi}i=1n⊆Spec(mif);2.whenever κ has uncountable cofinality, it is consistent that Spec (mif) = { ℵ1, κ= c}. Assuming large cardinals, in addition to (1) above, we can provide that (κi,κi+1)∩Spec(mif)=∅for each i, 1 ≤ i< n.

Original languageEnglish
Pages (from-to)877-884
Number of pages8
JournalArchive for Mathematical Logic
Volume58
Issue number7-8
DOIs
StatePublished - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, The Author(s).

Keywords

  • Cardinal characteristics
  • Independent families
  • Sacks indestructibility
  • Spectrum
  • Ultrapowers

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