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"Rupert" <rupertmccallum@xxxxxxxxx> writes:
> aatu.koskensilta@xxxxxxxxx wrote:
>> Rupert wrote:
>> > There is no definable well-ordering of the reals.
>>
>> That's certainly true. It is consistent with ZFC that there is a
>> definable well-ordering of the universe (and thus also of the reals),
>> though.
>>
>
> I may have expressed myself poorly. I think the result I wanted to cite
> was "no expression can be proved in ZF to define a well-ordering of the
> reals, assuming that ZF is consistent." Is that known?
attributed to Dana Scott in Bell's "Boolean-valued models and
independence proofs in Set Theory":
"if ZF is consistent, so is ZF + GCH + no definable well-ordering of
power set of omega."
>> --
>> Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
>>
>> "Wovon man nicht sprechen kann, daruber muss man schweigen"
>> - Ludwig Wittgenstein, Tractatus Logic-Philosophicus
>
--
Alan Smaill
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