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On two problems of Erdos and Hechler: New methods in singular Madness
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 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