$\aleph_k$-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
Daniel Herden
Baylor University, Waco, USA
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