Non-existence of universal members in classes of abelian groups

Details Non-existence of universal members in classes of abelian groups Non-existence of universal members in classes of abelian groups

1998-08-15

arxiv.org/abs/math/9808139v1

Mathematics

Logic

Scientific paper

We prove that if mu^+< lambda =cf(lambda)< mu^{aleph_0}, then there is no universal reduced torsion free abelian group. Similarly if aleph_0< lambda < 2^{aleph_0}. We also prove that if 2^{aleph_0}< mu^+< lambda =cf(lambda)< mu^{aleph_0}, then there is no universal reduced separable abelian p-group in lambda. (Note: both results fail if lambda = lambda^{aleph_0} or if lambda is strong limit, cf (mu)= aleph_0< mu).

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