[FOM] A question about \omega-consistent theories
steve newberry
stevnewb at att.net
Tue Apr 28 14:58:52 EDT 2009
Form new theory PRA+ by adding ~W (the negation of the omega-rule W) to PRA . Since W has no finite models, ~W has no finite counter-models and is valid on every finite domain, and hence is inductively valid.
Since W + PRA is simply consistent but omega-inconsistent, ~W is not provable in PRA, and hence not true in the standard model of PA.
Steve Newberry
--- On Mon, 4/27/09, Arnon Avron <aa at tau.ac.il> wrote:
> From: Arnon Avron <aa at tau.ac.il>
> Subject: [FOM] A question about \omega-consistent theories
> To: fom at cs.nyu.edu
> Date: Monday, April 27, 2009, 9:06 AM
> 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)?
>
> Thanks
>
> Arnon Avron
>
>
>
> ----------------------------------------------------------------
> Prof. Arnon Avron | +972-3-640-6352 Office
> School of Computer Science | +972-3-640-6352 Fax
> Tel Aviv University | +972-3-641-0043 Home
> Tel Aviv, 69978 | +972-3-640-8040
> secretary
> ISRAEL | email: aa at math.tau.ac.il
> |
> http://www.math.tau.ac.il/~aa/
> ----------------------------------------------------------------
>
>
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
More information about the FOM
mailing list