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user 14094
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Which abelian groups are $\aleph_1$-filtered colimits of finitely-generated abelian groups?
Yes. This can be rephrased as: let $G$ be an abelian group [resp. group] with a chain of f.g. subgroups $G_\alpha$ for $\alpha<\omega_1$. Is $G$ f.g.?
The answer is yes for abelian groups:
The answer …
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