Some ugly aleph_1-free abelian groups

Details Some ugly aleph_1-free abelian groups Some ugly aleph_1-free abelian groups

2001-07-29

arxiv.org/abs/math/0107208v1

Mathematics

Logic

Scientific paper

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 Godel'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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