Sh:521

• Shelah, S. (1996). If there is an exactly \lambda-free abelian group then there is an exactly \lambda-separable one in \lambda. J. Symbolic Logic, 61(4), 1261–1278. arXiv: math/9503226 DOI: 10.2307/2275815 MR: 1456106
• Abstract:
  We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly \lambda-free ones was proved earlier by the criteria in [Sh:161] in [MkSh:251]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups.
• Version 1995-03-10_10 (21p) published version (19p)

@article{Sh:521,
 author = {Shelah, Saharon},
 title = {{If there is an exactly $\lambda$-free abelian group then there is an exactly $\lambda$-separable one in $\lambda$}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {61},
 number = {4},
 year = {1996},
 pages = {1261--1278},
 issn = {0022-4812},
 mrnumber = {1456106},
 mrclass = {20K20 (03E75 08B20)},
 doi = {10.2307/2275815},
 note = {\href{https://arxiv.org/abs/math/9503226}{arXiv: math/9503226}},
 arxiv_number = {math/9503226}
}