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Strong measure zero sets without Cohen reals

Martin Goldstern·Haim Judah·Saharon Shelah
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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.

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Martin Goldstern, Haim Judah, Saharon Shelah. 1993-06-15. Strong measure zero sets without Cohen reals. https://arxiv.org/abs/math/9306214

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