Timeline for Existence of well-ordering of epsilon_0 in weak theories
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Oct 26, 2022 at 9:43 | history | suggested | C7X |
Gentzen's consistency proof
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| Oct 26, 2022 at 8:33 | review | Suggested edits | |||
| S Oct 26, 2022 at 9:43 | |||||
| Mar 6, 2017 at 19:18 | vote | accept | David Roberts♦ | ||
| Mar 6, 2017 at 16:17 | answer | added | Emil Jeřábek | timeline score: 10 | |
| Mar 6, 2017 at 16:05 | comment | added | Andreas Blass | The comment from @EmilJeřábek answers the question, but it might be worthwhile to amplify it to say "but those theories and even PA itself cannot prove it is a well order." | |
| Mar 6, 2017 at 10:50 | comment | added | David Roberts♦ | @EmilJeřábek or, perhaps you mean the order type of $\varepsilon_0$ can be defined in a weak fragment of PA, so we can consider $\varepsilon_0$ to be 'defined' in this way... | |
| Mar 6, 2017 at 9:39 | comment | added | David Roberts♦ | @Emil this is exactly the sort of answer I'm after. Details would be good, to settle the argument conclusively. I don't even care about the ordering, merely the existence of $\varepsilon_0$, but the actual definition is perhaps important for my purposes. | |
| Mar 6, 2017 at 9:19 | comment | added | Emil Jeřábek | I'm not sure I understand the question. The order on $\epsilon_0$ as such can be constructed in very weak fragments of PA, but those theories cannot prove it is a well order (i.e., satisfies appropriate forms of induction). | |
| Mar 6, 2017 at 8:23 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
added 2 characters in body
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| Mar 6, 2017 at 7:16 | history | asked | David Roberts♦ | CC BY-SA 3.0 |