Re: Why can't such an example be given?
- From: Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx>
- Date: Thu, 15 May 2008 14:39:54 GMT
On 2008-05-13, in sci.math, Herman Rubin wrote:
In article <%7eWj.151$_03.39@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx> wrote:
Any explicit example we could provide would have to rely on
principles beyond those contained in ZFC. If we assume the axiom of
constructibility, for example, there is a definable well-ordering of
the reals
Definitely NOT. Such a well-ordering would easily enable
Vitali's example to be constructed.
(and even of the whole universe),
This is equivalent to the axiom of choice.
To the global axiom of choice, yes. I'm baffled by your objection
above; that there is a definable well-ordering of the constructible
universe is precisely what is established in the standard proofs of
consistency of the axiom of choice.
--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
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