Title
The spectrum of independence
Author
Saharon Shelah
Einstein Institute of Mathematics, The Hebrew University of Jerusalem
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}ni=1⊆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
Keywords
Cardinal characteristicsIndependent familiesSpectrumSacks indestructibilityUltrapowers
Object type
Language
English [eng]
Persistent identifier
Appeared in
Title
Archive for Mathematical Logic
Volume
58
Issue
7-8
From page
877
To page
884
Publication
Springer Science and Business Media LLC
Version type
Date issued
2019
Access rights
Rights
Rights statement
© The Author(s) 2019
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