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From: Frode Bjørdal on 1 Jun 2010 16:15
On 1 Jun, 21:50, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Frode Bjørdal <fbenlightenment4...(a)gmail.com> writes:
> > Does this not depend on the notion of model being involved? E.g.,
> > could one not in some weak theory have a model of ZF in the sense that
> > it has a set of the Gödel numbers which code a theorem of ZF, while
> > this set of Gödel numbers for ZF is still a well-founded set of
> > standard natural numbers?
>
> I'm afraid I don't understand your question. What does it mean for a
> theory to have a set of Gödel numbers?

I am just thinking about natural numbers. Subsystems of second order
arithmetic will have such sets, based on various Aussonderung
principles. But they are also strong enough to provide various codings
of provability predicates.
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