[FOM] A question about \omega-consistent theories
pax0 at seznam.cz
Mon Apr 27 15:11:38 EDT 2009
Arnon Avron wrote:
> Can anybody give me an example of a (not necessarily recursive
> or r.e.) \omega-consistent theory in the language of PA which
> proves all true quantifiers-free sentences in this language,
> but also some sentence which is not true (in the standard model of PA)?
Just take the theory
where omega-con is the formalized property of being omega consistent.
This theory proves all true Q.F. sentences (by Sigma_1-completeness of PA),
but omega(PA) is presumably true.
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