Nielsen‐Schreier and the Axiom of Choice

Mathematical Logic Quarterly 61 (6):458-465 (2015)
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Abstract

The Nielsen‐Schreier theorem asserts that subgroups of free groups are free. In the first section we show that this theorem does not follow from the Linear Ordering Principle, thus strengthening the fact that it implies the Axiom of Choice for families of finite sets. In the second section, we show that a stronger variant of the Nielsen‐Schreier theorem implies the Axiom of Choice.

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10.1002/malq.201400046

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References found in this work

Subgroups of a free group and the axiom of choice.Paul E. Howard - 1985 - Journal of Symbolic Logic 50 (2):458-467.
The Existence of Level Sets in a Free Group Implies the Axiom of Choice.Paul E. Howard - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):315-316.

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