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arXiv · 1804.05538

Deeply concatenable subgroups might never be free

Samuel M. Corson·Saharon Shelah
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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

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Samuel M. Corson, Saharon Shelah. 2018-04-16. Deeply concatenable subgroups might never be free. https://arxiv.org/abs/1804.05538

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