On strong measure zero subsets of {}^kappa 2 .
Logic
2009-09-25 v1
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.
Cite
@article{arxiv.math/9710218,
title = {On strong measure zero subsets of {}^kappa 2 .},
author = {Aapo Halko and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9710218},
year = {2009}
}