Re: what makes it true?

Torkel Franzen <torkel@xxxxxxxxxx> wrote:
>Ben Rudiak-Gould <br276deleteme@xxxxxxxxx> wrote:
>>
>> So you can't resolve the question of which one is really true
>> by using models, because it will depend on your choice of model.
>
> In order to prove some arithmetical statement A not provable in PA,
> what we need is to use some mathematical principles not formalizable
> in PA. 0+0=0 is undecidable in the theory PA' obtained by leaving out
> the axiom "for every n, n+0=n" from PA, but that doesn't mean that we
> need to concern ourselves with models of PA'+"not-0+0=0" in order to
> decide whether 0+0=0.

Which axiomatization of PA do you refer to above?

--Bill Dubuque
.

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