On two problems of Erdos and Hechler: New methods in singular Madness
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.