  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.
