  This paper answers three questions posed by the first author. In Theorem 2.6
we show that the family of strong measure zero subsets of {}^{omega_1}2 is
2^{aleph_1}-additive under GMA and CH. In Theorem 3.1 we prove that the
generalized Borel conjecture is false in {}^{omega_1}2 assuming ZFC+CH. Next,
in Theorem 4.2, we show that the family of subsets of {}^{omega_1}2 with the
property of Baire is not closed under the Souslin operation.
