Re: Provable in T?
- From: "Rupert" <rupertmccallum@xxxxxxxxx>
- Date: 13 Aug 2006 16:40:03 -0700
Rupert wrote:
Newberry wrote:
Aatu Koskensilta wrote:
Newberry wrote:
What is the status of this?
"G_T is true in the standard model"
It's not clear what you're asking.
Is it the case that G_T is true in the standard model? If so, how do we
know it is the case? I presume "G_T is true in the standard model" is
not provable.
Do we need to say "If T is consistent then G_T is true in the standard
model"?
If T is consistent, then G_T will be true in the standard model and
also provable in T+Con(T).
It will be provable in T+Con(T), provided T extends Sigma-1-Induction
Arithmetic, I should say.
However, T+Con(T) may not be consistent. But
if T is sound it will be.
.
- References:
- Provable in T?
- From: bargiax
- Re: Provable in T?
- From: Aatu Koskensilta
- Re: Provable in T?
- From: Newberry
- Re: Provable in T?
- From: Aatu Koskensilta
- Re: Provable in T?
- From: Newberry
- Re: Provable in T?
- From: Rupert
- Provable in T?
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