### 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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