Timeline for What is induction up to $\varepsilon_0$?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| May 31, 2023 at 22:20 | comment | added | cody | and $\mathrm{PA}$ does not prove that induction up to $\epsilon_0$ is well-founded for any "reasonable" notation system for it, though it can express that statement. | |
| May 31, 2023 at 22:18 | comment | added | cody | $\epsilon_0$ does have a finitary representation of a similar sort! It is a computable ordinal and quite low on the Veblen hierarchy (see e.g. this). However it does not have a Cantor normal form (and is the first such ordinal), so the notation needs to be different from that one. | |
| Jul 24, 2019 at 20:55 | comment | added | Thomas Benjamin | @DavidE.Speyer: Since on your blog post, $\omega^{\omega}$ is represented by the list (((()))), is there some reason why $\epsilon_0$ cannot have a 'finitary' representation of a similar sort? | |
| Dec 7, 2009 at 16:25 | history | answered | David E Speyer | CC BY-SA 2.5 |