> There is an infinite cascade of provable
> theorems of, say, number theory.
But what if you declare theorems which say the same thing to be the
_same theorem_, rewritten?
Duraid
But this reference does not say what you say.
There is an infinite cascade of provable
theorems of, say, number theory.
> From Hal Ruhl <[EMAIL PROTECTED]> Wed Apr 11 05:02:30 2001:
> For the cite to Chaitin see "The Limits to Mathematics" page 17 note 1 at
> the bottom of the page.
Hal, Chaitin just says "you cannot prove 20 pound theorems with 10 pound
axioms". But the infinite cascade of all provable theorems of number
theory collectively does not convey more information than the axioms.
> But what if you declare theorems which say the same thing to be the
> _same theorem
Sorry I think an unedited version of this may have got out by mistake. I
have not seen it get posted so perhaps it did not. Again if it did I am sorry.
Dear Juergen:
At 4/10/01, you wrote:
>Hal, you wrote:
>
> > I believe that attempting an extensive detailed formal description of
> > the Eve
Dear Juergen:
At 4/11/01, you wrote:
>Hal, Chaitin just says "you cannot prove 20 pound theorems with 10 pound
>axioms".
Please refer to Chaitin's "The Unknowable" generally and page 25, Chapter
V, and note 10 at the bottom of page 97 in particular.
>But the infinite cascade of all provable th
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