Open Access
Spring/Summer 2003 On the existence of precovers
Paul C. Eklof, Saharon Shelah
Illinois J. Math. 47(1-2): 173-188 (Spring/Summer 2003). DOI: 10.1215/ijm/1258488146


It is proved consistent with ZFC + GCH that for every Whitehead group $A$ of infinite rank, there is a Whitehead group $H_{A}$ such that $\operatorname{Ext} (H_{A},A)\neq 0$. This is a strong generalization of the consistency of the existence of non-free Whitehead groups. A consequence is that it is undecidable in ZFC + GCH whether every $\mathbb{Z}$-module has a $^{\perp }\{ \mathbb{Z\}}$-precover. Moreover, for a large class of $\mathbb{Z}$-modules $ N$, it is proved consistent that a known sufficient condition for the existence of $^{\perp }\{N\}$-precovers is not satisfied.


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Paul C. Eklof. Saharon Shelah. "On the existence of precovers." Illinois J. Math. 47 (1-2) 173 - 188, Spring/Summer 2003.


Published: Spring/Summer 2003
First available in Project Euclid: 17 November 2009

zbMATH: 1033.20065
MathSciNet: MR2031314
Digital Object Identifier: 10.1215/ijm/1258488146

Primary: 20K40
Secondary: 03E35

Rights: Copyright © 2003 University of Illinois at Urbana-Champaign

Vol.47 • No. 1-2 • Spring/Summer 2003
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