Timeline for Derivation rules and Godel theorem
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2010 at 1:31 | comment | added | Joel David Hamkins | If you are interested in just one model, then why have a formal proof system at all? One would want instead just to check truth in that model. | |
| Jun 28, 2010 at 15:21 | comment | added | Bogdan Grechuk | Thank you. You wrote "To have a sound rule, you should accompany it by a change in what counts as a legitimate model". So, I may say "lets add my rule D to PA and consider only standard model"? Now, in standard model new rule (and hence new theory) is sound, can prove (in one step) its own consistency, and, as pointed out by Professor Carl Mummert, Godel Theorem is not applicable for this theory. This is interesting... May be, adding new rules of deduction to well-known theories could help us to create new, more powerful theories, valid not in all models, but in "interesting" ones. | |
| Jun 28, 2010 at 15:20 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Corrected treatment of PA
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| Jun 28, 2010 at 14:24 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 555 characters in body; added 75 characters in body
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| Jun 28, 2010 at 14:14 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Added Reflection theorem argument; deleted 294 characters in body
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| Jun 28, 2010 at 13:42 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |