# 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.
• 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.
• published version (17p)
Bib entry
@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}
}