Return to Question

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?

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?

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?

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?