Timeline for Terminology for ordinals whose constructible level is the least one satisfying some formula
Current License: CC BY-SA 4.0
7 events
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May 15, 2023 at 13:06 | comment | added | Johan | I looked around a bit and it happened to be also very close from the notion of characterizability mostly used in infinitary and second order logic. I gave some examples of uses in my answer. | |
May 5, 2023 at 21:50 | vote | accept | Johan | ||
Apr 23, 2023 at 3:35 | comment | added | Jason Zesheng Chen | Joel, it seems to me that the sup of these metadefinable ordinals is exactly the first 1-stable. The key observation is that it's $\Sigma_1$ to say that a specific metadefinable ordinal is countable, and so there'll be an ordinal meta-defined by the ability to see this collapse map. This implies that the supremum $\sigma$ will have $L_\sigma$ ($\Sigma_1$-)pointwise definable. But then any $\Sigma_1$ formula true in $L$ with parameters from $L_\sigma$ is equivalent to a $\Sigma_1$ sentence. And so it must be true in some $L_\beta$ below $L_\sigma$ and hence in $L_\sigma$ by upward absoluteness. | |
Apr 22, 2023 at 12:20 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
improve exposition and fix grammar issues
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Apr 21, 2023 at 22:51 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 233 characters in body
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Apr 21, 2023 at 22:44 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
added 1007 characters in body
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Apr 21, 2023 at 22:27 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |