# 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. 229â€“286. arXiv: math/9609217 MR: 1683540 -
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 nonâ€“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} }