### Cotorsion theories cogenerated by $\aleph_1$ free Abelian groups

by Shelah and Struengmann. [ShSm:773]

Rocky Mountain J Math, 2002

Given an aleph_1-free abelian group G we characterize the
class C_G of all torsion abelian groups T satisfying
Ext (G,T)=0 assuming the continuum hypothesis CH. Moreover, in
G{o}del's constructable universe we prove that this characterizes
C_G for arbitrary torsion-free abelian G . It follows
that there exist some ugly aleph_1-free abelian groups.

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