Sujet : Re: Analytic Truth-makers
De : wasell (at) *nospam* example.com (Wasell)
Groupes : comp.theory sci.logicDate : 23. Jul 2024, 15:51:57
Autres entêtes
Organisation : Never You Mind, Inc.
Message-ID : <MPG.4109e1eeb98e7f829896fe@reader.eternal-september.org>
References : 1 2 3 4
User-Agent : MicroPlanet-Gravity/3.0.4
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>
…