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arXiv · 1909.00595

$\aleph_k$-free cogenerators

Manfred Dugas·Daniel Herden·Saharon Shelah
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Abstract

We prove in ZFC that an abelian group $C$ is cotorsion if and only if $\operatorname{Ext}(F,C) = 0$ for every $\aleph_k$-free group $F$, and discuss some consequences and related results. This short note includes a condensed overview of the $\bar\lambda$-Black Box for $\aleph_k$-free constructions in ZFC.

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Manfred Dugas, Daniel Herden, Saharon Shelah. 2019-09-02. $\aleph_k$-free cogenerators. https://arxiv.org/abs/1909.00595

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