# Sh:662

- Halko, A., & Shelah, S. (2001).
*On strong measure zero subsets of ^\kappa2*. Fund. Math.,**170**(3), 219–229. arXiv: math/9710218 DOI: 10.4064/fm170-3-1 MR: 1880900 -
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} }