# 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. arXiv: math/9204219 DOI: 10.1007/BF02808073 MR: 1202574 -
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. - 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}, doi = {10.1007/BF02808073}, mrclass = {20K20 (03E05 03E35 20A15)}, mrnumber = {1202574}, mrreviewer = {U. Felgner}, doi = {10.1007/BF02808073}, note = {\href{https://arxiv.org/abs/math/9204219}{arXiv: math/9204219}}, arxiv_number = {math/9204219} }