# 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.
• 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)
Bib entry
@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}
}