Archive for Mathematical Logic 58 (7-8):877-884 (2019)

We study the set of possible sizes 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.Péter Komjáath - 2000 - Bulletin of Symbolic Logic 6 (1):83-86.

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Ideals of Independence.Vera Fischer & Diana Carolina Montoya - 2019 - Archive for Mathematical Logic 58 (5-6):767-785.

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