English

MAD Families and SANE Player

Logic 2010-07-19 v3

Abstract

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.

Keywords

Cite

@article{arxiv.0904.0816,
  title  = {MAD Families and SANE Player},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:0904.0816},
  year   = {2010}
}
R2 v1 2026-06-21T12:48:23.547Z