Dear Russell:
At 4/13/01, you wrote:
>Bounded complexity does not imply bounded length. Examples include an
>infinite sting of '0's, and the string '1234...9101112...'

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That was part of the old debate and one of my initial mistakes. I am not
now talking about the length of theorems but the length of their proofs.
>It must be true that the set of all theorems derivable from a finite
>set of axioms contains no more information (or complexity) than is
>contained in the set of axioms itself. However, as pointed out, this
>doesn't imply the theorems are bounded in length, merely that their
>complexity is bounded.
>
>Does this shed light on this issue?
With this I agree. There are however only a finite number of theorems
with a finite complexity. So number theory is either finite in theorem
count or it is infinite in complexity.
Hal