Admissible
A set \(M\) is admissible if \((M,\in)\) is a model of Kripke-Platek set theory. An ordinal \(\alpha\) is admissible if there exists an admissible set \(M\) such that \(M\cap\textrm{Ord}=\alpha\). This definition of admissibility is equivalent to \(L_\alpha\vDash\textrm{KP}\).[1]
- ↑ Probably in Barwise somewhere