The spectrum of independence

Archive for Mathematical Logic:1-7 (forthcoming)

We study the set of possible size of maximal independent families to which we refer as spectrum of independence and denote \\). Here mif abbreviates maximal independent family. We show that:1.whenever \ are finitely many regular uncountable cardinals, it is consistent that \\); 2.whenever \ has uncountable cofinality, it is consistent that \=\{\aleph _1,\kappa =\mathfrak {c}\}\). Assuming large cardinals, in addition to above, we can provide that $$\begin{aligned} \cap \hbox {Spec}=\emptyset \end{aligned}$$for each i, \.
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DOI 10.1007/s00153-019-00665-y
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References found in this work BETA

Con(U>I).Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (6):433-443.
Proper and Improper Forcing.Saharon Shelah - 2000 - Bulletin of Symbolic Logic 6 (1):83-86.

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Ideals of Independence.Vera Fischer & Diana Carolina Montoya - forthcoming - Archive for Mathematical Logic:1-19.

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