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Paper: chao-dyn/9407009
From: chaitin@watson.ibm.com
Date: Sat, 23 Jul 94 10:32:38 EDT

Title: The Limits of Mathematics---Fourth Version
Author: G.J. Chaitin (IBM Research Division)
Comments: 231 pages, LaTeX, ignore numerous Overfull hbox too wide errors
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Abstract: This is yet another version of the course notes in
chao-dyn/9407003.  Here we use m-expressions more aggressively to
further reduce the constants in our information-theoretic
incompleteness theorems.  Our main theorems are: 1) an N-bit formal
axiomatic system cannot enable one to exhibit any specific object with
program-size complexity greater than N+c, 2) an N-bit formal axiomatic
system cannot enable one to determine more than N+c' scattered bits of
the halting probability Omega.  In chao-dyn/9407003, c = 2359 bits and
c' = 7581 bits.  In chao-dyn/9407005, c = 1127 bits and c' = 3689
bits.  In chao-dyn/9407006, c = 994 bits and c' = 3192 bits.  And in
this version, c = 735 bits and c' = 2933 bits.
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