# Sh:438

- Goldstern, M., Judah, H. I., & Shelah, S. (1993).
*Strong measure zero sets without Cohen reals*. J. Symbolic Logic,**58**(4), 1323–1341. arXiv: math/9306214 DOI: 10.2307/2275146 MR: 1253925 -
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.

- 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}, doi = {10.2307/2275146}, mrclass = {03E35 (04A15 04A20)}, mrnumber = {1253925}, mrreviewer = {Jakub Jasi\'nski}, doi = {10.2307/2275146}, note = {\href{https://arxiv.org/abs/math/9306214}{arXiv: math/9306214}}, arxiv_number = {math/9306214} }