The spectrum of independence
Copyright policy )The spectrum of independence
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 κ 1< ⋯ < κ n 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) = { ℵ 1, 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.
- University of Vienna Austria
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- Universität Wien Austria
- Universität Wien Austria
- Hebrew University of Jerusalem Israel
101013 Mathematical logic, Cardinal characteristics, Independent families, Spectrum, 101013 Mathematische Logik, Sacks indestructibility, Ultrapowers
101013 Mathematical logic, Cardinal characteristics, Independent families, Spectrum, 101013 Mathematische Logik, Sacks indestructibility, Ultrapowers
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