Non-existence of universal members in classes of abelian groups
Logic
2009-09-25 v1
Abstract
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).
Keywords
Cite
@article{arxiv.math/9808139,
title = {Non-existence of universal members in classes of abelian groups},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9808139},
year = {2009}
}