Sh:772

• Shelah, S., & Strüngmann, L. H. (2003). Kulikov’s problem on universal torsion-free abelian groups. J. London Math. Soc. (2), 67(3), 626–642. arXiv: math/0112253 DOI: 10.1112/S0024610703004216 MR: 1967696
• Abstract:
  Let T be an abelian group and \lambda an uncountable regular cardinal. We consider the question of whether there is a \lambda-universal group G^* among all torsion-free abelian groups G of cardinality less than or equal to \lambda satisfying {\rm Ext}(G,T)=0. Here G^* is said to be \lambda-universal for T if, whenever a torsion-free abelian group G of cardinality less than or equal to \lambda satisfies {\rm Ext}(G,T)=0, then there is an embedding of G into G^*. For large classes of abelian groups T and cardinals \lambda it is shown that the answer is consistently no. In particular, for T torsion, this solves a problem of Kulikov.
• Version 2001-07-11_11 (16p) published version (17p)

@article{Sh:772,
 author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
 title = {{Kulikov's problem on universal torsion-free abelian groups}},
 journal = {J. London Math. Soc. (2)},
 fjournal = {Journal of the London Mathematical Society. Second Series},
 volume = {67},
 number = {3},
 year = {2003},
 pages = {626--642},
 issn = {0024-6107},
 mrnumber = {1967696},
 mrclass = {20K40 (20K20 20K35)},
 doi = {10.1112/S0024610703004216},
 note = {\href{https://arxiv.org/abs/math/0112253}{arXiv: math/0112253}},
 arxiv_number = {math/0112253}
}