Timeline for Most general formulation of Gödel's incompleteness theorems
Current License: CC BY-SA 2.5
8 events
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| Dec 18, 2017 at 5:13 | comment | added | user21820 | Indeed there is typically a gap, and this post gives the full generalization of the first incompleteness theorem, where basically all you need is that the formal system has a proof verifier program and can prove every true $Σ_1$-sentence (under some computable translation). To get the second incompleteness theorem, you could require it to uniformly interpret PA as defined here, so that you can get Lob's theorem (internally). | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jul 20, 2010 at 19:34 | vote | accept | Sebastian Reichelt | ||
| Jul 19, 2010 at 9:11 | answer | added | user7247 | timeline score: 16 | |
| Jul 18, 2010 at 9:59 | answer | added | Charles Stewart | timeline score: 9 | |
| Jul 18, 2010 at 0:25 | answer | added | Michaël | timeline score: 5 | |
| Jul 17, 2010 at 23:18 | comment | added | Sidney Raffer | Have a look at Smullyan's "Theory of Formal Systems" and "Godel's Incompleteness Theorems". The first book studies the phenomenon in very primitive forms of "deductive systems" and the second presents generalizations via modal logic. | |
| Jul 17, 2010 at 22:09 | history | asked | Sebastian Reichelt | CC BY-SA 2.5 |