On two problems of Erdös and Hechler: New methods in singular madness

Menachem Kojman, Wiesław Kubiś, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


For an infinite cardinal μ, MAD(μ) denotes the set of all cardinalities of nontrivial maximal almost disjoint families over μ. Erd̈os and Hechler proved in 1973 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 cf 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.

Original languageEnglish
Pages (from-to)3357-3365
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number11
StatePublished - 1 Nov 2004


  • Almost disjoint family
  • Bounding number
  • Singular cardinal
  • Smooth pcf scales

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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