The cardinal characteristic for relative γ-sets

  title={The cardinal characteristic for relative γ-sets},
  author={Arnold W. Miller},
For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γset in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(2) and p(ω) in terms of definable free filters on ω which is related to the pseudo-intersection number p. We show that for every uncountable standard analytic space X that either p(X) = p(2) or p(X) = p(ω). We show that the following statements are each relatively consistent… CONTINUE READING