Existence of Vector Space Bases implies Axiom of Choice
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Theorem
The supposition that every vector space has a basis, along with the Zermelo-Fraenkel axioms, implies that the axiom of choice holds.
Proof
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Sources
- 1984: Andreas Blass: Existence of Bases implies the Axiom of Choice (Contemporary Mathematics Vol. 31: pp. 31 – 33)