  In this paper we show that it is relatively consistent with ZFC that every
gamma-set is countable while not every strong measure zero set is countable.
This answers a question of Paul Szeptycki. A set is a gamma-set iff every
omega-cover contains a gamma-subcover. An open cover is an omega-cover iff
every finite set is covered by some element of the cover. An open cover is a
gamma-cover iff every element of the space is in all but finitely many elements
of the cover. Gerlits and Nagy proved that every gamma-set has strong measure
zero. We also show that is consistent that every strong gamma-set is countable
while there exists an uncountable gamma-set. On the other hand every strong
measure zero set is countable iff every set with the Rothberger property is
countable.
