[FOM] Is there a reasonable sense in which PA is complete?

Harvey Friedman friedman at math.ohio-state.edu
Sun Oct 29 00:23:35 EDT 2006

On 10/28/06 6:26 PM, "Martin Davis" <davism at cs.nyu.edu> wrote:

> Friedman Harvey wrote:
>> ***Under any reasonable measure of complexity of sentences in the language
>> of PA, any sentence or scheme in the language of PA of modest complexity is
>> either provable or refutable in PA.***
> This assertion surprises me. I for one don't believe it, and see no compelling
> evidence for it considering the large number of such sentences that have
> remained unresolved despite great interest.

Not a single one of them is of reasonable complexity as sentences or schemes
in the primitive language of PA with 0,S,+,x.

I hope to find the time to work on this.


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