Title: The cardinal characteristic for relative gamma-sets
Author: Arnold W. Miller
Abstract: For $X$ a separable metric space define $\pp(X)$ to be
the smallest cardinality of a subset $Z$ of $X$ which is not a
relative $\ga$-set in $X$, i.e., there exists an $\om$-cover of
$X$ with no $\ga$-subcover of $Z$. We give a characterization of
$\pp(2^\om)$ and $\pp(\om^\om)$ in terms of definable free filters
on $\om$ which is related to the psuedointersection number
$\pp$. We show that for every uncountable standard analytic
space $X$ that either $\pp(X)=\pp(2^\om)$ or $\pp(X)=\pp(\om^\om)$.
We show that both of following statements are each relatively
consistent with ZFC:
(a) $\pp=\pp(\om^\om) < \pp(2^\om)$ and
(b) $\pp < \pp(\om^\om) =\pp(2^\om)$
LaTeX: 14 pages