Almost disjoint families and property (a)

Volume 158 / 1998

Paul J. Szeptycki, Jerry E. Vaughan Fundamenta Mathematicae 158 (1998), 229-240 DOI: 10.4064/fm-158-3-229-240


We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < \got p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).


  • Paul J. Szeptycki
  • Jerry E. Vaughan

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