# Sh:935

• Shelah, S. (2011). MAD saturated families and SANE player. Canad. J. Math., 63(6), 1416–1435.
• Abstract:
We throw some light on the question: is there a MAD family (= a family of infinite subsets of \mathbb N, the intersection of any two is finite) which is completely separable (i.e. any X \subseteq \mathbb N is included in a finite union of members of the family 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.
• Current version: 2015-06-02_12 (23p) published version (20p)
Bib entry
@article{Sh:935,
author = {Shelah, Saharon},
title = {{MAD saturated families and SANE player}},
}