Philipp Kleppmann
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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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.
Key concepts: Axiom of choice, Zermelo–Fraenkel set theory, Axiom independence, Urelement, Mathematics, Statement (logic), Axiom, Constructive set theory