Generating sets of free groups and the axiom of choice

Mathematical Logic Quarterly 60 (3):239-241 (2014)
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Abstract

Write F(X) for the free group generated by X. We show that the statement for infinite sets is equivalent to the Axiom of Choice, whereas the statement is strictly weaker than the Axiom of Choice.

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10.1002/malq.201300088

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References found in this work

The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
Subgroups of a free group and the axiom of choice.Paul E. Howard - 1985 - Journal of Symbolic Logic 50 (2):458-467.

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