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Jun 18, 2023 at 7:36 comment added Joel David Hamkins I agree, but $L_\xi$ is definable in all the later limit stages of the OPs construction in which $\xi$ is definable, since the set $L_\xi$ itself validates all the earlier stages of construction, and if $\xi$ is a successor then the top level will be definable, since the truth predicate of $L_\xi$ is definable.
Jun 18, 2023 at 6:14 comment added Monroe Eskew It seems one needs to find $\alpha$ such that the definition of $L_\xi$ is absolute to $L_\alpha$. Or is this not really an issue?
Jun 17, 2023 at 12:55 history edited Joel David Hamkins CC BY-SA 4.0
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Jun 16, 2023 at 13:35 vote accept Zuhair Al-Johar
Jun 16, 2023 at 13:29 history answered Joel David Hamkins CC BY-SA 4.0