Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non existence of universals for classes like reduced torsion free
  abelian groups under non neccessarily pure embeddings   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.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol