# 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. arXiv: math/0406552 DOI: 10.1007/BF02937512 MR: 1303496 -
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. - Version 2000-10-27_10 (23p) 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}, mrnumber = {1303496}, mrclass = {20K20 (03E05 03E35)}, doi = {10.1007/BF02937512}, note = {\href{https://arxiv.org/abs/math/0406552}{arXiv: math/0406552}}, arxiv_number = {math/0406552} }