Deeply concatenable subgroups might never be free

by Corson and Shelah. [CrSh:1142]

We show that certain algebraic structures lack freeness in the absence of the axiom of choice. These include some subgroups of the Baer-Spevcker group {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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