aleph_k$-free cogenerators

aleph_k$-free cogenerators

We prove in ZFC that an abelian group $C$ is cotorsion if and only if 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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Veröffentlicht in:Rendiconti - Seminario matematico della Università di Padova 2020-12, Vol.144, p.87-104
Hauptverfasser: Dugas, Manfred, Herden, Daniel, Shelah, Saharon
Format: Artikel
Sprache:eng
Schlagworte:
Commutative rings and algebras
Group theory and generalizations
Mathematical logic and foundations
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Zusammenfassung:We prove in ZFC that an abelian group $C$ is cotorsion if and only if 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.
ISSN:0041-8994
2240-2926
DOI:10.4171/RSMUP/58