[FOM] Only one proof (fwd)

[John Baldwin]

On Mon, 31 Aug 2009, Aatu Koskensilta wrote:

  Quoting William Tait <williamtait at mac.com>:
>
> > Two examples in set theory are Goedel's proof of the consistency of CH
> > relative to ZF using inner models and Cohen's proof of the consistency
> > of Not-CH using forcing.
>
> Another example: Gdel's proof for the first incompleteness theorem
> understood as the result that the set of Pi-1 truths is productive.
> I'm not aware of any way of proving this result without going through
> essentially the recursion theoretic contortions found in the original
> proof. (I may well be just ignorant.)
>
I am not sure of how `understood as productive' affects the observation 
that via Paris-Harrington,
the first incompleteness theorem can be proved without coding syntax. 
This surely qualifies as a
different proof.





John T. Baldwin
Emeritus Professor
Department of Mathematics, Statistics, and Computer
Science
jbaldwin at uic.edu
312-413-2149
Room 613 Science and Engineering Offices (SEO)
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Chicago, IL 60607