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

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

2004-06-22

arxiv.org/abs/math/0406441v1

Mathematics

Logic

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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.

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