Hurewicz sets of reals without perfect subsets
  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. 
Du\v{s}an Repov\v{s}, Boaz Tsaban, and Lyubomyr Zdomskyy