Some ugly aleph₁-free abelian groups

2001/07/29 by Saharon Shelah, Shelah, Saharon, Lutz Strüngmann +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO

paper · pdf · doi:10.48550/arxiv.math/0107208

published as Rocky Mountain J. Math. 32 No. 4 (2002) 1617--1626

arxiv created 2001/07/29 · arxiv updated 2009/11/30

Abstract

Given an aleph₁-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 aleph₁-free abelian groups.

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