Strong measure zero sets without Cohen reals
Logic
2009-09-25 v1
Abstract
If ZFC is consistent, then each of the following are consistent with ZFC + 2^{{aleph_0}}= aleph_2 : 1.) X subseteq R is of strong measure zero iff |X| <= aleph_1 + there is a generalized Sierpinski set. 2.) The union of aleph_1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size aleph_2.
Cite
@article{arxiv.math/9306214,
title = {Strong measure zero sets without Cohen reals},
author = {Martin Goldstern and Haim Judah and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9306214},
year = {2009}
}