Re: Can transfinite (strong) induction for N be derived from Peano's Axioms?

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 02/24/05 

Date: 24 Feb 2005 21:54:21 GMT

H. Enderton <hbe@sonia.math.ucla.edu> wrote:
>Dan Christensen <dchris@allstream.net> wrote:
>>If so, can someone sketch out a proof starting from PA?
>
>First of all, I'm assuming "transfinite" was unintended.
>And that the topic is the strong induction schema:
> If (forall n)[(forall m < n)phi(m) --> phi(n)], then (forall n)phi(n)
>If my assumption is wrong, you can stop reading here.
>
>Yes, all instances of strong induction are provable in PA.
>Arturo Magidin already covered this...

How do you reconcile Bill Dubuque's complaints then? 

-- 
Mitch (remove the q to email)