The Limits of Mathematics---Fourth Version

Details The Limits of Mathematics---Fourth Version The Limits of Mathematics---Fourth Version

1994-07-23

arxiv.org/abs/chao-dyn/9407009v1

Nonlinear Sciences

Chaotic Dynamics

231 pages, LaTeX, ignore numerous Overfull hbox too wide errors

Scientific paper

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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