STRONG MEASURE ZERO SETS WITHOUT COHEN REALS

Authors
GOLDSTERN M JUDAH H SHELAH S
Citation
M. Goldstern et al., STRONG MEASURE ZERO SETS WITHOUT COHEN REALS, The Journal of symbolic logic, 58(4), 1993, pp. 1323-1341
Citations number
24
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
The Journal of symbolic logic → ACNP
ISSN journal
00224812
Volume
58
Issue
4
Year of publication
1993
Pages
1323 - 1341
Database
ISI
SICI code
0022-4812(1993)58:4<1323:SMZSWC>2.0.ZU;2-B
Abstract
If ZFC is consistent, then each of the following is consistent with ZF C + 2(aleph 0) = aleph(2): (1) X subset of or equal to R is of strong measure zero iff \X\ less than or equal to aleph(1) + there is a gener alized Sierpinski set. (2) The union of aleph(1) many strong measure z ero 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.