Published online by Cambridge University Press: 12 March 2014
If ZFC is consistent, then each of the following is consistent with :
(1) X ⊆ ℝ is of strong measure zero iff ∣X∣ ≤ ℵ1 + there is a generalized Sierpinski set.
(2) The union of ℵ 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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