Strong measure zero sets without Cohen reals
Martin Goldstern, Haim Judah, Saharon Shelah
Abstract
If ZFC is consistent, then each of the following are consistent with ZFC + 2aleph0= aleph2 : 1.) X subseteq R is of strong measure zero iff |X| <= aleph1 + there is a generalized Sierpinski set. 2.) The union of aleph1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size aleph2.
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