Re: Analytic Truth-makers

On Mon, 22 Jul 2024 20:17:15 -0400, in article
<3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>, Richard Damon wrote:

 
On 7/22/24 8:11 PM, olcott wrote:

[...]

*No stupid I have never been saying anything like that* If g and
~g is not provable in PA then g is not a truth-bearer in PA.

>
What makes it different fron Goldbach's conjecture?

I think a better example might be Goodstein's theorem [1].

* It is expressible in the same language as PA.

* It is neither provable, nor disprovable, in PA.

* We know that it is true in the standard model of arithmetic.

* We know that it is false in some (necessarily non-standard) models
  of arithmetic.

* It was discovered and proved long before it was shown to be
  undecidable in PA.

The only drawback is that the theorem is somewhat more complicated
than Goldbach's conjecture -- not a lot, but a bit.


[1] <https://en.wikipedia.org/wiki/Goodstein%27s_theorem>