## Journal of Symbolic Logic

### Strong Measure Zero Sets without Cohen Reals

#### Abstract

If ZFC is consistent, then each of the following is consistent with $\mathrm{ZFC} + 2^{\aleph_0} = \aleph_2$: (1) $X \subseteq \mathbb{R}$ is of strong measure zero $\mathrm{iff} |X| \leq \aleph_1 +$ 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 $\aleph_2 +$ there is no Cohen real over $L$.

#### Article information

Source
J. Symbolic Logic, Volume 58, Issue 4 (1993), 1323-1341.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744378

Mathematical Reviews number (MathSciNet)
MR1253925

Zentralblatt MATH identifier
0794.03067

JSTOR