Re: Which axiom prohibits this kind of construction?
- From: Starblade Enkai <StarbladeEnkai@xxxxxxxxxx>
- Date: Wed, 8 Oct 2008 21:33:21 -0700 (PDT)
On Sep 30, 2:11 am, Aatu Koskensilta <aatu.koskensi...@xxxxxx> wrote:
Virgil <Vir...@xxxxxxxxx> writes:
But the set of all subsets of an infinite set like the set of naturals
has no explicit well-ordering, and while it may be theoretically
well-orderable given the axiom of choice, it supposed to be impossible
to actually /construct/ one.
Enkai'sworry was that in presence of foundation the levels of the
cumulative hierarchy might not be well-ordered, that there might be an
infinite descending sequence of levels of the cumulative hierarchy.
--
Aatu Koskensilta (aatu.koskensi...@xxxxxx)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Yes, I'm pretty sure I meant that. So wouldn't this be forbidden,
since z = [y] = [[x]] = [[[w]]] = ... and so on infinitely?
.
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