Strong Measure Zero Sets without Cohen Reals
Goldstern, Martin ; Judah, Haim ; Shelah, Saharon
J. Symbolic Logic, Tome 58 (1993) no. 1, p. 1323-1341 / Harvested from Project Euclid
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If ZFC is consistent, then each of the following is consistent with $\mathrm{ZFC} + 2^{\aleph_0} = \aleph_2$: (1) $X \subseteq \mathbb{R}$ is of strong measure zero $\mathrm{iff} |X| \leq \aleph_1 +$ 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 $\aleph_2 +$ there is no Cohen real over $L$.
Publié le : 1993-12-14
Classification:  
@article{1183744378,
     author = {Goldstern, Martin and Judah, Haim and Shelah, Saharon},
     title = {Strong Measure Zero Sets without Cohen Reals},
     journal = {J. Symbolic Logic},
     volume = {58},
     number = {1},
     year = {1993},
     pages = { 1323-1341},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744378}
}

Goldstern, Martin; Judah, Haim; Shelah, Saharon. Strong Measure Zero Sets without Cohen Reals. J. Symbolic Logic, Tome 58 (1993) no. 1, pp.  1323-1341. http://gdmltest.u-ga.fr/item/1183744378/