Some ugly aleph1-free abelian groups
Saharon Shelah, Lutz Strüngmann
Abstract
Given an aleph1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G,T)=0 assuming the continuum hypothesis CH. Moreover, in Godel's constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly aleph1-free abelian groups.
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