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Let $\mathbf{L}_{\varsigma}$ be the level of ordinal $\varsigma$ of Gödel's constructible universe $\mathbf{L}$. Let $\Sigma_{3}$-KP be Kripke-Platek set theory with infinity and $\Sigma_{3}$-$collection$ and $\Sigma_{3}$-$comprehension$. Let $\sigma$ be the least ordinal such that $\mathbf{L}_{\sigma}$ models $\Sigma_{3}$-KP. If $\sigma$ is not a $\Sigma_{3}$-admissible ordinal, then what is it?

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    $\begingroup$ Isn't this by definition $\Sigma_3$-admissible ordinal? $\endgroup$
    – Wojowu
    Nov 15, 2014 at 12:35
  • $\begingroup$ That may well be, and I thought so as well. Perhaps I misunderstood a comment in a communication. May someone else confirm, so that I perhaps should delete the question? Does someone have references to literature on this? $\endgroup$ Nov 15, 2014 at 16:58

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