On two problems of Erd\H os and Hechler: New methods in singular Madness

by Kojman and Kubis and Shelah. [KKSh:793]
Proc American Math Soc, 2004
For an infinite cardinal mu, MAD (mu) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over mu . Erd{o}s 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.

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