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*needed*in the case of the reals? That is, if we remove the axiom of choice, do the reals become a set that cannot be well-ordered? Furthermore, is the axiom of choice needed for every uncountable set?

- Thread starter dmuthuk
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CRGreathouse

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Yes, I believe I am. So, I guess what I wanted to know is if there exists a proof that the reals can be well-ordered without AC.

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No there isn't. When Cohen proved the independence of AC he used a model in which there was no well-ordering of the reals.Yes, I believe I am. So, I guess what I wanted to know is if there exists a proof that the reals can be well-ordered without AC.

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CRGreathouse

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* By "consistent", I mean "equiconsistent with ZFC".

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