Re: A Possible Additional Axiom Schema for PA ?

From: Jeffrey Ketland (ketland_at_ketland.fsnet.co.uk)
Date: 02/02/05 

Date: Wed, 2 Feb 2005 20:08:23 -0000

Helene.Boucher@wanadoo.fr

>I thought "induction instance" means
>
>(x)(phi(x) => phi(x'))
>
>But then phi(x) as (x > n) is obviously a counterexample to your
>assertion. Since this is not likely to be a mistake you would make,
>could I ask what you mean by "induction instance" ?

"Induction instance" means

[phi(0) & (Ax)(phi(x) -> phi(S(x)))] -> (Ax)phi(x)

For a simple example, suppose you refute phi(0). Then you prove the above.

--- Jeff

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