Timeline for Hyperarithmetically least elements in $\Pi^1_1$ sets
Current License: CC BY-SA 4.0
5 events
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| Nov 20, 2023 at 3:09 | comment | added | Farmer S | The pointwise definability is because the theory includes "$V=L$" + KP. Given any model $M$ of "$V=L$" plus some basic set theory included in KP, the definable hull of $M$ (the collection of elements of $M$ definable over $M$) is elementary in $M$ and is pointwise definable. For the second point, it can be seen in Theorem 4F.1 in Moschovakis "Descriptive set theory", 2nd ed. | |
| Nov 19, 2023 at 19:52 | comment | added | Hanul Jeon | Thank you for your interesting answer, and let me ask a question about the facts in your argument. You used the two facts "Every $T\in X$ has a pointwise definable model" and "If $A$ is $\Sigma^1_1$ and $A\nsubseteq L_{\omega_1^{CK}}$ then $A$ has a perfect subset." Is there any reference for these facts? | |
| Nov 19, 2023 at 5:35 | vote | accept | Hanul Jeon | ||
| Nov 19, 2023 at 2:08 | history | edited | Farmer S | CC BY-SA 4.0 |
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| Nov 19, 2023 at 2:02 | history | answered | Farmer S | CC BY-SA 4.0 |