# Sh:793

• Kojman, M., Kubiś, W., & Shelah, S. (2004). On two problems of Erdős and Hechler: new methods in singular madness. Proc. Amer. Math. Soc., 132(11), 3357–3365.
• Abstract:
For an infinite cardinal \mu, {\rm MAD}(\mu) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over \mu. Erdős and Hechler proved the consistency of \mu\in {\rm MAD}(\mu) for a singular cardinal \mu and asked if it was ever possible for a singular \mu that \mu\notin {\rm MAD}(\mu), and also whether 2^{{\rm cf}\mu}<\mu\Longrightarrow\mu\in{\rm MAD} (\mu) for every singular cardinal \mu.

We introduce a new method for controlling {\rm MAD}(\mu) for a singular \mu and, among other new results about the structure of {\rm MAD}(\mu) for singular \mu, settle both problems affirmatively.

• Current version: 2004-05-17_11 (10p) published version (9p)
Bib entry
@article{Sh:793,
author = {Kojman, Menachem and Kubi{\'s}, Wies{\l}aw and Shelah, Saharon},
title = {{On two problems of Erd\H{o}s and Hechler: new methods in singular madness}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {132},
number = {11},
year = {2004},
pages = {3357--3365},
issn = {0002-9939},
mrnumber = {2073313},
mrclass = {03E05 (03E04 03E17 03E35 03E55)},
doi = {10.1090/S0002-9939-04-07580-X},
note = {\href{https://arxiv.org/abs/math/0406441}{arXiv: math/0406441}},
arxiv_number = {math/0406441}
}