### Strong measure zero sets without Cohen reals

by Goldstern and Judah and Shelah. [GJSh:438]

J Symbolic Logic, 1993

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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