## General recursion theory: an axiomatic approach |

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### Contents

On the Choice of Correct Notions for the General Theory | 3 |

Combinatorial Part | 19 |

Subcomputations | 43 |

Copyright | |

8 other sections not shown

### Common terms and phrases

0-computable function 0-computable mapping 0-finite set 0-Mahlo 0-semicomputable relations 0-semicomputable set admissible sets argument assume assumption axiomatic basic Chapter characteristic function clause computation domain computation set computation theory construction countable Definition domain 91 element enumeration exists F-recursive finite functional F hence higher types hyperarithmetic hyperarithmetic theory immediate subcomputations induction hypothesis inductive definability inductive operator infinite theory introduced Kechris Kleene L-subconstructive least fixed-point Lemma limit ordinal monotone Moschovakis natural numbers normal type-2 notation notion ordinal p-normal partial function PR(L PR[f PR[g precomputation theory prewellordering prewellordering property prime computation primitive recursive primitive recursive function proof Proposition prove quantifiers R-admissible reader recursion in higher recursion theory recursive function Remark requirement result Section selection operator sequence set-recursive Spector class Spector theory stage subset theory on 91 total functions tuples type-2 functional weakly 0-computable well-foundedness wellordering