# Sh:438

• Goldstern, M., Judah, H. I., & Shelah, S. (1993). Strong measure zero sets without Cohen reals. J. Symbolic Logic, 58(4), 1323–1341.
• 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| \leq \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.

• Version 1993-08-29_10 (27p) published version (20p)
Bib entry
@article{Sh:438,
author = {Goldstern, Martin and Judah, Haim I. and Shelah, Saharon},
title = {{Strong measure zero sets without Cohen reals}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {58},
number = {4},
year = {1993},
pages = {1323--1341},
issn = {0022-4812},
mrnumber = {1253925},
mrclass = {03E35 (04A15 04A20)},
doi = {10.2307/2275146},
note = {\href{https://arxiv.org/abs/math/9306214}{arXiv: math/9306214}},
arxiv_number = {math/9306214}
}