## Higher recursion theory |

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### Contents

Part A Hyperarithmetic Sets | 1 |

Constructive Ordinals and n Sets | 3 |

Notations for Ordinals | 8 |

Copyright | |

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### Common terms and phrases

a-cardinal a-finite a-recursive a-stable admissible ordinal admissible set admits Moschovakis witnesses arithmetic Assume L(k bounded classical recursion theory closed closure co^K cofinality Corollary countable definition denoted effective transfinite recursion element encodes enumerable on L(k equivalent Exercise exists a recursive follows formula Gandy selection gc(a Godel number Hence hyperarithmetic hierarchy hyperarithmetic sets hyperdegree hyperregular implies induction initial segment injury Kleene Kleene's Kreisel Lemma metafinite metarecursion theory metarecursive function metarecursively enumerable set natural enumeration negative requirements nonempty Normann notations one-one open set order definable ordertype ordinals less parameters partial recursive function Post's problem prior to stage projectum proof of Lemma proof of Theorem Proposition proved quantifiers recursive ordinals recursively enumerable sets regular relativization req 2e satisfies Section Show solution to Post's Spector subset Suppose TC(x Theorem 4.1 tp(a tp(S Turing Turing degrees Turing jump Turing reducibility unbounded unique wellfounded wellordering