# Sh:662

• Halko, A., & Shelah, S. (2001). On strong measure zero subsets of ^\kappa2. Fund. Math., 170(3), 219–229.
• Abstract:
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.
• Version 2001-01-23_10 (15p) published version (11p)
Bib entry
@article{Sh:662,
author = {Halko, Aapo and Shelah, Saharon},
title = {{On strong measure zero subsets of $^\kappa2$}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {170},
number = {3},
year = {2001},
pages = {219--229},
issn = {0016-2736},
mrnumber = {1880900},
mrclass = {03E15 (03E05)},
doi = {10.4064/fm170-3-1},
note = {\href{https://arxiv.org/abs/math/9710218}{arXiv: math/9710218}},
arxiv_number = {math/9710218}
}