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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.
>
> --
> Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
>
> "Wovon man nicht sprechen kann, daruber muss man schweigen"
> - Ludwig Wittgenstein, Tractatus Logic-Philosophicus
I wonder what you mean by that, Aatu. There are no universes in ZF.
There are features of the real numbers not often used in the standard.
Yeah, well-order the reals.
Some published papers have the reals being well-ordered, recent ones.
It's consistent that the cardinality of the reals is Aleph_1, Aleph_2,
..., then they're each equivalent. How's that for a continuum
hypothesis? Ha ha ha.
Ross
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