# Sh:935

- Shelah, S. (2011).
*MAD saturated families and SANE player*. Canad. J. Math.,**63**(6), 1416–1435. arXiv: 0904.0816 DOI: 10.4153/CJM-2011-057-1 MR: 2894445 -
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. - Version 2015-06-02_12 (23p) published version (20p)

Bib entry

@article{Sh:935, author = {Shelah, Saharon}, title = {{MAD saturated families and SANE player}}, journal = {Canad. J. Math.}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques}, volume = {63}, number = {6}, year = {2011}, pages = {1416--1435}, issn = {0008-414X}, mrnumber = {2894445}, mrclass = {03E05 (03E17 03E40)}, doi = {10.4153/CJM-2011-057-1}, note = {\href{https://arxiv.org/abs/0904.0816}{arXiv: 0904.0816}}, arxiv_number = {0904.0816} }