Skip to main content
7 events
when toggle format what by license comment
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
Apr 21, 2023 at 22:51 history edited Joel David Hamkins CC BY-SA 4.0
added 233 characters in body
Apr 21, 2023 at 22:44 history edited Joel David Hamkins CC BY-SA 4.0
added 1007 characters in body
Apr 21, 2023 at 22:27 history answered Joel David Hamkins CC BY-SA 4.0