# Sh:552

• Shelah, S. (1997). Non-existence of universals for classes like reduced torsion free abelian groups under embeddings which are not necessarily pure. In Advances in algebra and model theory (Essen, 1994; Dresden, 1995), Vol. 9, Gordon; Breach, Amsterdam, pp. 229–286.
• Abstract:
We consider a class K of structures e.g. trees with \omega+1 levels, metric spaces and mainly, classes of Abelian groups like the one mentioned in the title and the class of reduced separable (Abelian) p-groups. We say M\in K is universal for K if any member N of K of cardinality not bigger than the cardinality of M can be embedded into M. This is a natural, often raised, problem. We try to draw consequences of cardinal arithmetic to non–existence of universal members for such natural classes.
• Version 2002-04-03_11 (51p) published version (58p)
Bib entry
@incollection{Sh:552,
author = {Shelah, Saharon},
title = {{Non-existence of universals for classes like reduced torsion free abelian groups under embeddings which are not necessarily pure}},
booktitle = {{Advances in algebra and model theory (Essen, 1994; Dresden, 1995)}},
series = {Algebra Logic Appl.},
volume = {9},
year = {1997},
pages = {229--286},
publisher = {Gordon and Breach, Amsterdam},
mrnumber = {1683540},
mrclass = {20K27 (03E75 20A15)},
note = {\href{https://arxiv.org/abs/math/9609217}{arXiv: math/9609217}},
arxiv_number = {math/9609217}
}