# 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. arXiv: math/0406441 DOI: 10.1090/S0002-9939-04-07580-X MR: 2073313 -
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.

- 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} }