Alpha recursion theory

Summary

In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals $\alpha$. An admissible set is closed under $\Sigma_1(L_\alpha)$ functions, where $L_\xi$ denotes a rank of Godel's constructible hierarchy. $\alpha$ is an admissible ordinal if $L_{\alpha}$ is a model of Kripke–Platek set theory. In what follows $\alpha$ is considered to be fixed.