An equivalent of the axiom of choice in finite models of the powerset axiom

Notre Dame Journal of Formal Logic 31 (3):371-374 (1990)
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Mitchell Spector (1988). Ultrapowers Without the Axiom of Choice. Journal of Symbolic Logic 53 (4):1208-1219.
Harvey Friedman (2000). Does Mathematics Need New Axioms? Bulletin of Symbolic Logic 6 (4):401 - 446.
John L. Bell, The Axiom of Choice. Stanford Encyclopedia of Philosophy.
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