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
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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}
}