Timeline for What are some proofs of Godel's Theorem which are *essentially different* from the original proof?
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17 events
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| Jun 11 at 17:53 | answer | added | Noah Schweber | timeline score: 1 | |
| May 15, 2022 at 9:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
replaced the dead link
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| Mar 1, 2020 at 6:05 | answer | added | Noah Schweber | timeline score: 3 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 5, 2013 at 0:31 | answer | added | Eliezer Yudkowsky | timeline score: 5 | |
| Aug 5, 2011 at 20:50 | comment | added | Kaveh | @Emil, you are correct, I take back my comment, I forgot the part that we need to show that $T \vdash "T\nvdash G"$ implies $T\vdash G$, there might be some way of doing it more generally but I don't see it. | |
| Aug 5, 2011 at 16:03 | comment | added | Emil Jeřábek | @Kaveh: That’s quite a bold claim. Why do you think this should be true? The usual derivation of the 2nd theorem by formalizing the 1st one uses some quite idiosyncratic features of Gödel’s proof: (1) unprovability of Gödel’s sentence $G$, unlike its negation, only needs the consistency of the theory rather than $\Sigma_1$-soundness or whatever stronger assumption, and (2) the provability of unprovability of $G$ implies the provability of $G$ (because $G$ happens to be defined so that it is provably equivalent to its own unprovability). | |
| Aug 5, 2011 at 15:45 | comment | added | Emil Jeřábek | Kripke’s proof is interesting, however it only works for extensions of PA in the language of PA, which is a rather uninteresting class of theories. It does not apply to fragments of PA, and it does not apply to theories whose language includes objects that are not integers (such as ZFC or ACA_0). That’s not what I would call an alternate proof of Gödel’s first incompleteness theorem, but rather of its very special case. | |
| Aug 5, 2011 at 6:09 | answer | added | Ron Maimon | timeline score: 38 | |
| Aug 5, 2011 at 3:01 | answer | added | Sergei Tropanets | timeline score: 0 | |
| Aug 4, 2011 at 18:37 | answer | added | Gerald Edgar | timeline score: 0 | |
| Aug 4, 2011 at 15:11 | answer | added | Andrew Marks | timeline score: 5 | |
| Aug 4, 2011 at 13:52 | comment | added | Michaël | Did you have a look to this recent blog post of Scott? scottaaronson.com/blog/?p=710 | |
| Aug 4, 2011 at 4:43 | comment | added | Ron Maimon | Godel's original proof does not use full omega consistency. He only needs a small fragment, namely that if the axiom system proves a program P halts, then P actually halts. This is sigma-0-1 soundness. | |
| Aug 4, 2011 at 4:15 | answer | added | Michael Hardy | timeline score: 2 | |
| Aug 4, 2011 at 4:05 | history | edited | Noah Schweber |
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| Aug 4, 2011 at 3:35 | history | asked | Noah Schweber | CC BY-SA 3.0 |