Timeline for Situation with Artemov's paper?
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Jul 28 at 0:07 | history | edited | Sergei Artemov | CC BY-SA 4.0 |
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| Jul 27 at 17:10 | comment | added | Timothy Chow | @SergeiArtemov I have now posted my question, which you said makes perfect sense, as a separate MO question. | |
| Jul 24 at 1:45 | comment | added | Sergei Artemov | This is correct. But with a bit deeper coding, we can get away with a single numeral code. Since $\textsf{Con}^S(\textsf{PA})$ is defined by its formula $\neg (x:\bot)$, the Godel number of the latter may be regarded as a code of the whole scheme. It all depends on what we want to do with the codes. | |
| Jul 24 at 0:40 | comment | added | David Roberts♦ | @SergeiArtemov I suspect Philippe was asking if $\mathrm{Con}^S(\textsf{PA})$ had a single Gödel number, or not. With the "for all $n$" outside the statement it seems like it should have a sequence of Gödel numbers, one for each $n$. But this is only my naive reading. | |
| Jul 23 at 19:52 | comment | added | Sergei Artemov | To Philippe Gaucher. A special class of serial properties generated by some arithmetical formula F(x) is called "schemes." They have perfectly well-defined Goedel numbers. Example: the consistency scheme $\mathrm{Con}^S(\textsf{PA})$ is generated by the formula $\neg x:\bot$. | |
| Jul 23 at 19:16 | history | edited | Sergei Artemov | CC BY-SA 4.0 |
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| Jul 23 at 19:10 | history | edited | Sergei Artemov | CC BY-SA 4.0 |
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| Jul 23 at 16:32 | comment | added | Sergei Artemov | Thank you! Your question makes perfect sense (except for the weird "your proposed definition of "consistency""; it is the common definition of consistency used by Hilbert). In short, my work dismounts the unprovability of consistency thesis (that a consistent theory cannot prove its own consistency), removing the principal obstacle for Hilbert's Program. This is our humble contribution. | |
| Jul 23 at 13:49 | comment | added | Timothy Chow | Welcome to MO! I have a question, which perhaps I can post as a separate MO question if your answer is too long for a comment. You mention Hilbert's program. As I understand it, Hilbert hoped for a PRA proof of the consistency of a set-theoretic system such as ZF. With your proposed definition of "consistency," what are the prospects for that? | |
| Jul 23 at 5:21 | comment | added | Philippe Gaucher | I have a very naive question. Intuitively, this means that you put the "for all n" outside the statement defining consistency. So the serial property $Con^S(PA)$ has no Gödel numbering. Is it correct ? | |
| Jul 23 at 3:11 | history | edited | Sergei Artemov | CC BY-SA 4.0 |
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| S Jul 22 at 23:37 | review | First answers | |||
| Jul 23 at 0:03 | |||||
| S Jul 22 at 23:37 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Missed a bit
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| Jul 22 at 23:33 | review | Late answers | |||
| Jul 22 at 23:35 | |||||
| Jul 22 at 23:30 | comment | added | Joel David Hamkins | Welcome to MathOverflow, Sergei. | |
| Jul 22 at 23:28 | comment | added | David Roberts♦ | I took the liberty of nicely formatting your text, and fixing a small conflict between the Markdown syntax and what one is used to from (La)TeX. Thank you for the clarification regarding the status of your paper. This is indeed very interesting. | |
| Jul 22 at 23:27 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Formatting
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| Jul 22 at 23:20 | comment | added | David Roberts♦ | Welcome to MathOverflow, Prof. Artemov! I guess JLC = Journal of Logic and Computation? | |
| S Jul 22 at 23:17 | review | First answers | |||
| Jul 22 at 23:35 | |||||
| S Jul 22 at 23:17 | history | answered | Sergei Artemov | CC BY-SA 4.0 |