Non-existence of universal members in classes of abelian groups
Saharon Shelah
Abstract
We prove that if mu+< lambda =cf(lambda)< mualeph0, then there is no universal reduced torsion free abelian group. Similarly if aleph0< lambda < 2aleph0. We also prove that if 2aleph0< mu+< lambda =cf(lambda)< mualeph0, then there is no universal reduced separable abelian p-group in lambda. (Note: both results fail if lambda = lambdaaleph0 or if lambda is strong limit, cf (mu)= aleph0< mu).
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