On Two Problems of Erdős and Hechler: New Methods in Singular Madness
نویسنده
چکیده
For an infinite cardinal μ, MAD(μ) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over μ. Erdős and Hechler proved in [7] the consistency of μ ∈ MAD(μ) for a singular cardinal μ and asked if it was ever possible for a singular μ that μ / ∈ MAD(μ), and also whether 2 μ < μ =⇒ μ ∈ MAD(μ) for every singular cardinal μ. We introduce a new method for controlling MAD(μ) for a singular μ and, among other new results about the structure of MAD(μ) for singular μ, settle both problems affirmatively.
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