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Re: Axiomatization of Ordinal Arithmetic

Subject: Re: Axiomatization of Ordinal Arithmetic
From: "Peter_Smith"
Date: 29 Oct 2006 01:51:39 -0700
Newsgroups: sci.logic
Charlie-Boo wrote:

> > > It's much easier (better by Occam's Razor) to see that Peano's Axioms
> > > amount to the assertion that the set of natural numbers is recursively
> > > enuerable.  Do you agree to this equivalence?

When you say that one claim (or set of claims) "amounts to" another
claim, that is a naturally read as an equivalence claim. I pointed out
that, quite trivially, to say that PA applies to the X's and to say
that the X's are r.e. are not equivalent claims (there are instances of
X for which the first is false and the second true). So what do you
mean?

Of course, utterly trivially, the natural numbers are r.e.: I'm not
denying that! I'm just denying that the PA axioms "amount to" that
triviality.


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