Strong measure zero sets without Cohen reals

Journal of Symbolic Logic 58 (4):1323-1341 (1993)
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Abstract

If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L

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References found in this work

The borel conjecture.Haim Judah, Saharon Shelah & W. H. Woodin - 1990 - Annals of Pure and Applied Logic 50 (3):255-269.
Some notes on iterated forcing with $2^{\aleph0}>\aleph2$. [REVIEW]Saharon Shelah - 1987 - Notre Dame Journal of Formal Logic 29 (1):1-17.

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