Nielsen-Schreier implies the finite Axiom of Choice
Philipp Kleppmann
TL;DR
This paper demonstrates that the algebraic property that every subgroup of a free group is free leads to the logical conclusion that the Axiom of Choice holds for finite sets.
Contribution
It establishes a novel logical connection between a fundamental algebraic property and the Axiom of Choice for finite sets.
Findings
The subgroup property implies the finite Axiom of Choice.
New proof linking algebraic and set-theoretic principles.
Highlights the foundational significance of free groups.
Abstract
We present a new proof that the statement 'every subgroup of a free group is free' implies the Axiom of Choice for finite sets.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Game Theory and Voting Systems