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  "body": "\n## Summary\n\nIn 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.\n",
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