# Sh:442

• Eklof, P. C., Mekler, A. H., & Shelah, S. (1994). Hereditarily separable groups and monochromatic uniformization. Israel J. Math., 88(1-3), 213–235.
• Abstract:
We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality \aleph_1. This can be used, together with a known combinatorial equivalent of the existence of a non-free Whitehead group, to prove that it is consistent that every Whitehead group is free but not every hereditarily separable group is free. We also show that the fact that {\mathbb Z} is a p.i.d. with infinitely many primes is essential for this result.
• published version (23p)
Bib entry
@article{Sh:442,
author = {Eklof, Paul C. and Mekler, Alan H. and Shelah, Saharon},
title = {{Hereditarily separable groups and monochromatic uniformization}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {88},
number = {1-3},
year = {1994},
pages = {213--235},
issn = {0021-2172},
doi = {10.1007/BF02937512},
mrclass = {20K20 (03E05 03E35)},
mrnumber = {1303496},
mrreviewer = {U. Felgner},
doi = {10.1007/BF02937512},
note = {\href{https://arxiv.org/abs/math/0406552}{arXiv: math/0406552}},
arxiv_number = {math/0406552}
}