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From: Russell Standish <R.Standish.domain.name.hidden>

Date: Fri, 13 Apr 2001 10:46:31 +1000 (EST)

Hal Ruhl wrote:

*>
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*>
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*> >Basically, Hal believes a finite FAS by definition implies that each
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*> >theorem is constrained to be no more than N-bits in length.
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*>
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*> Well more precisely that the shortest possible proof chain of any theorem
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*> of a finite FAS can not be more complex than the limit which Chaitin
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*> provides. Is this not Chaitin's position? Given that, then there are only
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*> a finite number of theorems that satisfy this limit on the complexity of
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*> their shortest proof chains.
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*>
*

Bounded complexity does not imply bounded length. Examples include an

infinite sting of '0's, and the string '1234...9101112...'

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?

Cheers

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

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Received on Thu Apr 12 2001 - 18:19:39 PDT

Date: Fri, 13 Apr 2001 10:46:31 +1000 (EST)

Hal Ruhl wrote:

Bounded complexity does not imply bounded length. Examples include an

infinite sting of '0's, and the string '1234...9101112...'

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?

Cheers

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit, Phone 9385 6967

UNSW SYDNEY 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Thu Apr 12 2001 - 18:19:39 PDT

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