$\aleph_k$-free cogenerators

Manfred Dugas; Daniel Herden; Saharon Shelah

doi:10.4171/rsmup/58

JournalsrsmupVol. 144pp. 87–104

$ℵ_{k}$ -free cogenerators

Manfred Dugas
Baylor University, Waco, USA
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Daniel Herden
Baylor University, Waco, USA
- MathSciNet
- zbMATH Open
Saharon Shelah
The Hebrew University of Jerusalem, Israel and The State University of New Jersey, Piscataway, USA

$$\aleph_k$-free cogenerators cover$

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Abstract

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

Cite this article

Manfred Dugas, Daniel Herden, Saharon Shelah, $ℵ_{k}$ -free cogenerators. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 87–104

DOI 10.4171/RSMUP/58