aleph_k$-free cogenerators

aleph_k$-free cogenerators

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 i...

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Hauptverfasser: Dugas, Manfred, Herden, Daniel, Shelah, Saharon
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Group Theory
Mathematics - Logic
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Zusammenfassung: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.
DOI:10.48550/arxiv.1909.00595