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 . . . . . . an article on ZFC set theory will be forthcoming.  ZFC is ZF with the axiom of choice.  In the mean time, here is a link to Wikipedia

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Wikipedia: Axiom of choice

Related pages in this website

Zermelo–Fraenkel set theory (ZF set theory) -- Axioms of 1. extensionality, 2. regularity (foundation), 3. schema of specification (separation; restricted comprehension), 4. pairing, 5. union, 6. schema of collection, 7. infinity, 8. power set; Well-ordering theorem

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