The Limits of Mathematics---Fourth Version
| dc.creator | Chaitin, G. J. | |
| dc.date | 1994-07-23 | |
| dc.date.accessioned | 2026-07-07T09:07:43Z | |
| dc.date.available | 2026-07-07T09:07:43Z | |
| dc.description | 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. | |
| dc.description | 231 pages, LaTeX, ignore numerous Overfull hbox too wide errors | |
| dc.identifier | https://arxiv.org/abs/chao-dyn/9407009 | |
| dc.identifier | http://arxiv.org/abs/chao-dyn/9407009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150468 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | The Limits of Mathematics---Fourth Version | |
| dc.type | text |