  We study productive properties of gamma spaces, and their relation to other,
classic and modern, selective covering properties. Among other things, we prove
the following results:
  1. Solving a problem of F. Jordan, we show that for every unbounded tower set
of reals X of cardinality aleph_1, the space Cp(X) is productively FU. In
particular, the set X is productively gamma.
  2. Solving problems of Scheepers and Weiss, and proving a conjecture of
Babinkostova-Scheepers, we prove that, assuming CH, there are gamma spaces
whose product is not even Menger.
  3. Solving a problem of Scheepers-Tall, we show that the properties gamma and
Gerlits--Nagy (*) are preserved by Cohen forcing. Moreover, every Hurewicz
space that Remains Hurewicz in a Cohen extension must be Rothberger (and thus
(*)).
  We apply our results to solve a large number of additional problems, and use
Arhangel'skii duality to obtain results concerning local properties of function
spaces and countable topological groups.
