Sh:976

• Shelah, S., & Strüngmann, L. H. (2011). Kulikov’s problem on universal torsion-free abelian groups revisited. Bull. Lond. Math. Soc., 43(6), 1198–1204. DOI: 10.1112/blms/bdr055 MR: 2861541
• Abstract:
  Let $T$ be a torsion abelian group. We consider the class of all torsion-free abelian groups $G$ satisfying ${\rm Ext}(G,T)=0$ and search for $\lambda$-universal objects in this class. We show that for certain $T$ there is no $\omega$-universal group. However, for uncountable cardinals $\lambda$ there is always a $\lambda$-universal group if we assume $(V=L)$. Together with results by the second author this solves completely a problem by Kulikov.
• Version 2010-10-22_11 (8p) published version (7p)

@article{Sh:976,
 author = {Shelah, Saharon and Str{\"u}ngmann, Lutz H.},
 title = {{Kulikov's problem on universal torsion-free abelian groups revisited}},
 journal = {Bull. Lond. Math. Soc.},
 fjournal = {Bulletin of the London Mathematical Society},
 volume = {43},
 number = {6},
 year = {2011},
 pages = {1198--1204},
 issn = {0024-6093},
 mrnumber = {2861541},
 mrclass = {20K15 (20K20 20K35)},
 doi = {10.1112/blms/bdr055}
}