MAD Families and SANE Player

Details MAD Families and SANE Player MAD Families and SANE Player

2009-04-05

arxiv.org/abs/0904.0816v3

Mathematics

Logic

Scientific paper

We throw some light on the question: is there a MAD family (= a family of infinite subsets of N, the intersection of any two is finite) which is completely separable (i.e. any X subseteq N is included in a finite union of members of the family or include a member of the family). We prove that it is hard to prove the consistency of the negation: (a) if 2^{aleph_0} < aleph_omega, then there is such a family (b) if there is no such families then some situation related to pcf holds whose consistency is large.

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