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Ross A. Finlayson wrote:
> aatu.koskensilta@xxxxxxxxx wrote:
> > 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 wonder what you mean by that, Aatu. There are no universes in ZF.
That there is a definable well-ordering of the universe means that
there is a formula R(x,y) in the language of set theory such that
a) R is set-like, that is, for every set a, { x | R(x,a) } is a set
b) every non-empty set has an R-least element
Such an R exists e.g. if V=L, if V=L[0^#] and so forth.
> 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.
Very amusing.
--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logic-Philosophicus
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