Non existence of universals for classes like reduced torsion free abelian groups under non neccessarily pure embeddings

Details Non existence of universals for classes like reduced torsion free abelian groups under non neccessarily pure embeddings Non existence of universals for classes like reduced torsion free abelian groups under non neccessarily pure embeddings

1996-09-15

arxiv.org/abs/math/9609217v1

Mathematics

Logic

Scientific paper

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.

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