### On strong measure zero subsets of ${}^\kappa 2$.

by Halko and Shelah. [HkSh:662]

Fundamenta Math, 2001

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.

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