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).
• Version 2000-08-21_10 (29p) published version (23p)

@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},
 mrnumber = {1812323},
 mrclass = {20K27 (03E75 20A15)},
 doi = {10.1515/jgth.2001.014},
 note = {\href{https://arxiv.org/abs/math/9808139}{arXiv: math/9808139}},
 arxiv_number = {math/9808139}
}