---
tag: TF9NV9Z8N3
kind: concept
name: Alpha recursion theory
aliases: [alpha-recursion, recursion-theory]
sources:
  - wikipedia: en:12008116@r1345548712
    locator: Alpha recursion theory
    note: adopted
    mention: wikipedia://en/12008116
    sections: [Summary]
same_as:
  wikidata: Q4735170
  wikipedia: Alpha recursion theory
inventory: [2M8QHP0FNE]
---

## 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.