On two problems of Erdos and Hechler: New methods in singular Madness
Logic
2007-05-23 v1
Abstract
For an infinite cardinal mu, MAD(mu) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over mu. Erdos and Hechler proved the consistency of [mu in MAD(mu)] for a singular cardinal mu and asked if it was ever possible for a singular mu that [mu notin MAD(mu)], and also whether 2^{cf(mu)}<mu ===> [mu in MAD(mu)] for every singular cardinal mu. We introduce a new method for controlling MAD(mu) for a singular mu and, among other new results about the structure of MAD(mu) for singular mu, settle both problems affirmatively.
Cite
@article{arxiv.math/0406441,
title = {On two problems of Erdos and Hechler: New methods in singular Madness},
author = {Menahem Kojman and Wieslaw Kubis and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0406441},
year = {2007}
}