# Sh:622

- Shelah, S. (2001).
*Non-existence of universal members in classes of abelian groups*. J. Group Theory,**4**(2), 169–191. arXiv: math/9808139 DOI: 10.1515/jgth.2001.014 MR: 1812323 -
Abstract:

We prove that if \mu^+<\lambda=cf(\lambda)<\mu^{\aleph_0}, then there is no universal reduced torsion free abelian group. Similarly if \aleph_0<\lambda< 2^{\aleph_0}. We also prove that if 2^{\aleph_0}<\mu^+<\lambda=cf(\lambda)< \mu^{\aleph_0}, then there is no universal reduced separable abelian p-group in \lambda. (Note: both results fail if \lambda = \lambda^{\aleph_0} or if \lambda is strong limit, cf(\mu)=\aleph_0<\mu). - published version (23p)

Bib entry

@article{Sh:622, author = {Shelah, Saharon}, title = {{Non-existence of universal members in classes of abelian groups}}, journal = {J. Group Theory}, fjournal = {Journal of Group Theory}, volume = {4}, number = {2}, year = {2001}, pages = {169--191}, issn = {1433-5883}, doi = {10.1515/jgth.2001.014}, mrclass = {20K27 (03E75 20A15)}, mrnumber = {1812323}, mrreviewer = {Paul C. Eklof}, doi = {10.1515/jgth.2001.014}, note = {\href{https://arxiv.org/abs/math/9808139}{arXiv: math/9808139}}, arxiv_number = {math/9808139} }