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Some ugly aleph_1-free abelian groups

Saharon Shelah·Lutz Strüngmann
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Abstract

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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BibTeXRIS

Saharon Shelah, Lutz Strüngmann. 2001-07-29. Some ugly aleph_1-free abelian groups. https://arxiv.org/abs/math/0107208

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