# Sh:441

• Eklof, P. C., Mekler, A. H., & Shelah, S. (1992). Uniformization and the diversity of Whitehead groups. Israel J. Math., 80(3), 301–321.
• Abstract:
The connections between Whitehead groups and uniformization properties were investigated by the third author in [Sh:98]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, \aleph_1-coseparable) group of cardinality \aleph_1 if and only if there is a ladder system on a stationary subset of \omega_1 which satisfies 2-uniformization (respectively, omega-uniformization). These techniques allowed also the proof of various independence and consistency results about Whitehead groups, for example that it is consistent that there is a non-free Whitehead group of cardinality \aleph_1 but no non-free \aleph_1-coseparable group. However, some natural questions remained open, among them the following two: (i) Is it consistent that the class of W-groups of cardinality \aleph_1 is exactly the class of strongly \aleph_1-free groups of cardinality \aleph_1? (ii) If every strongly \aleph_1-free group of cardinality \aleph_1 is a W-group, are they also all \aleph_1-coseparable? In this paper we use the techniques of uniformization to answer the first question in the negative and give a partial affirmative answer to the second question.
• Version 1996-03-11_10 (19p) published version (21p)
Bib entry
@article{Sh:441,
author = {Eklof, Paul C. and Mekler, Alan H. and Shelah, Saharon},
title = {{Uniformization and the diversity of Whitehead groups}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {80},
number = {3},
year = {1992},
pages = {301--321},
issn = {0021-2172},
mrnumber = {1202574},
mrclass = {20K20 (03E05 03E35 20A15)},
doi = {10.1007/BF02808073},
note = {\href{https://arxiv.org/abs/math/9204219}{arXiv: math/9204219}},
arxiv_number = {math/9204219}
}