Timeline for The supremum of ordinals eventually writable by Ordinal Turing Machines with an oracle for the class of stabilization ordinals
Current License: CC BY-SA 4.0
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| Jul 12, 2022 at 8:21 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 7:54 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 7:48 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 7:23 | comment | added | SSequence | Also, I think it is probably reasonable to mention (very briefly) that you are talking about stabilization times with respect to first $\omega$ cells. | |
| Jul 12, 2022 at 7:20 | comment | added | SSequence | "Can we continue the similar logic unboundedly and define the class $\mathsf{S}$ of ordinals $\sigma(\beta)$, where $\beta$ may be an arbitrarily large ordinal?" I don't see any reason why we can't do this. To see this the following simple observation would suffice. Whenever arbitrarily large ordinals in $\mathrm{Ord}$ aren't marked as $1$ in an oracle tape we are guaranteed that we can take the supremum of stabilization times above all the $1$'s on the oracle tape (on the very least). This is also why the values $\sigma(\alpha)$ would be strictly increasing w.r.t. ordinal $\alpha$. | |
| Jul 12, 2022 at 6:08 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 5:45 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 5:35 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 5:13 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 4:58 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 4:49 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 4:38 | history | edited | lyrically wicked | CC BY-SA 4.0 |
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| Jul 12, 2022 at 4:16 | history | asked | lyrically wicked | CC BY-SA 4.0 |