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that for an admissible ordinal, the corresponding L-level is a model of KP? As it stands,
it is certainly false. <small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/79.235.170.206|79.235.170.206]] ([[User talk:79.235.170.206|talk]]) 21:00, 12 January 2015 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
== "An admissible set is closed under <math>\Sigma_1(L_\alpha)</math> functions ==
As it currently reads I think this claim is false, since for any admissible set <math>M</math>, if we take some <math>z\in M</math> and define <math>f(x)=\begin{cases}z\;\mathrm{if}\;x=z \\ \mathrm{undefined}\;\mathrm{otherwise}\end{cases}</math>, <math>f</math> is <math>\Sigma_1</math> on <math>M</math> but <math>M</math> is not closed under <math>f</math> (i.e. "<math>\forall(x\in M)\exists(y\in M)(y=f(x))</math>" is false, in fact "<math>\forall(x\in M)\exists y(y=f(x))</math>" is false.) The closest I can find to this in "The fine structure of the constructible hierarchy" is in the proof of lemma 2.13, where it says "but <math>X</math> is closed under <math>f</math> since <math>f</math> is <math>\Sigma_1</math> in <math>p\in X</math>. So I am not sure that there's a source for this claim. [[User:C7XWiki|C7XWiki]] ([[User talk:C7XWiki|talk]]) 07:01, 6 July 2023 (UTC)
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