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Re: Inconsistency
Posted:
Apr 22, 2012 12:34 PM
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Nam Nguyen wrote:
>
> On 22/04/2012 7:36 AM, Jan Burse wrote:
>
> >
> > Undecidable theories such as ZFC in general
> > don't admit a k.
>
> How would you know ZFC is undecidable in the first place?
A simple argument is as follows.
FOL with a single binary predicate is undecidable. (See Church, Turing,
and um... was it Kalmar?) And since ZFC is built on FOL with a single
binary predicate it is undecidable.
A better argument is to show that recursive functions are representable
in ZFC and proceed as you would in Robinson's Q or whatever. I say
'better' because that way the result about FOL with a single binary
predicate is a simple corollary.
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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