[FOM] A question about \omega-consistent theories

[steve newberry]

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
> 
> 
> 
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