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)

@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}
}