Timeline for Shortest proof of inconsistency of first order theory
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2021 at 8:37 | comment | added | Emil Jeřábek | Well, if there is a proof that $T$ is complete of length $n$, there is a proof that $T$ is inconsistent of length at most $n+c$, where $c$ is a constant (the length of the proof of Gödel’s theorem, basically). So it’s effectively almost the same. Thus, while it’s perfectly possible the answer to the question is yes, this might depend on some minute details of the definition of the proof system, and it might be quite difficult to prove, as usual speed-up theorems work with much bigger gaps than just an additive constant. | |
| Aug 19, 2021 at 8:05 | history | edited | siam | CC BY-SA 4.0 |
added 78 characters in body
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| Aug 19, 2021 at 8:05 | comment | added | siam | The time gap between the questions was more than 48 hours. I lost access to the old account. | |
| Aug 18, 2021 at 21:26 | comment | added | user44143 | This looks like an improved version of some questions that I commented on recently, that others downvoted, and that someone deleted -- so if the same person who asked those downvoted questions is asking a similar question here from a new account, I think that would be an abuse of the site, and asking improved questions from the same account would be more appropriate. | |
| Aug 18, 2021 at 17:49 | comment | added | Andreas Blass | You seem to be tacitly assuming that the theory in question is computably enumerable. Without such an assumption, there are plenty ($2^{\aleph_0}$) of complete, consistent theories extending PA or ZF. | |
| Aug 18, 2021 at 11:09 | review | First posts | |||
| Aug 18, 2021 at 11:42 | |||||
| Aug 18, 2021 at 11:05 | history | asked | siam | CC BY-SA 4.0 |