  We show that even for subsets X of the real line which do not contain perfect
sets, the Hurewicz property does not imply the property S1(Gamma,Gamma),
asserting that for each countable family of open gamma-covers of X, there is a
choice function whose image is a gamma-cover of X. This settles a problem of
Just, Miller, Scheepers, and Szeptycki.
  Our main result also answers a question of Bartoszynski and Tsaban, and
implies that for C_p(X), the conjunction of Sakai's strong countable fan
tightness and the Reznichenko property does not imply Arhangelskii's property
alpha_2.
