Equivalents of the axiom of choice

@inproceedings{Grabczewski2001EquivalentsOT,
  title={Equivalents of the axiom of choice},
  author={Krzysztof Grabczewski},
  year={2001}
}
Parts of this note have been discussed elsewhere in the blog, sometimes in a different form (see here and here, for example), but I haven’t examined before the equivalence of 5–7 with choice. In the course of the proof of the equivalence of item 7 with the other statements, a few additional equivalent versions of independent interest will be identified. The equivalence of 1–3 is classic. Zermelo’s original axiomatization of set theory intended to formalize the proof that 2⇒ 1. Statements 2 and… CONTINUE READING

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