Re: Peano arithmetic and transfinite induction

From: Keith Ramsay <kramsay@xxxxxxx>
Date: Sun, 26 Aug 2007 22:15:40 -0700

On Aug 25, 2:53 pm, djr...@xxxxxxxxxx wrote:
|However, I often find quotes such as: "It is
|evidently necessary to assume the validity of something like
|transfinite induction to prove the consistency of arithmetic".

As far as I can see, the only way in which these remarks
want to claim that the new axiom must be "like" transfinite
induction is in not being provable in PA (unless the author
is confused).

Keith Ramsay

.

References:
- Peano arithmetic and transfinite induction
  - From: djrt20

Prev by Date: Re: Continuum hypothesis
Next by Date: Finitely Valid Formula
Previous by thread: Re: Peano arithmetic and transfinite induction
Next by thread: Finitely Valid Formula
Index(es):
- Date
- Thread

Relevant Pages

Peano arithmetic and transfinite induction
... there is a diophantine diophantine equation which (iff PA is ... I often find quotes such as: ... evidently necessary to assume the validity of something like ... transfinite induction to prove the consistency of arithmetic". ...
(sci.logic)
Re: Peano arithmetic and transfinite induction
... there is a diophantine diophantine equation which (iff PA is ... evidently necessary to assume the validity of something like ... transfinite induction to prove the consistency of arithmetic". ...
(sci.logic)