Abstract
We show that certain algebraic structures lack freeness in the absence of the axiom of choice. These include some subgroups of the Baer–Specker group $\mathbb{Z}^{\omega}$ and the Hawaiian earring group. Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups are also presented.
Funding Statement
The first author was supported by European Research Council grant PCG-336983. The second author was partially supported by European Research Council grant 338821.
Citation
Samuel M. CORSON. Saharon SHELAH. "Deeply concatenable subgroups might never be free." J. Math. Soc. Japan 71 (4) 1123 - 1136, October, 2019. https://doi.org/10.2969/jmsj/80498049
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