## Degrees of UnsolvabilityDegrees of Unsolvability |

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### Contents

1 | |

3 | |

8 | |

Chapter 3 Algorithms | 12 |

Chapter 4 Relative Recursiveness | 15 |

Chapter 5 Recursive Enumerability | 20 |

Chapter 6 Degrees | 26 |

Chapter 7 Evaluating Degrees | 31 |

Chapter 10 The Jump Operation | 46 |

Chapter 11 Minimal Degrees | 49 |

Chapter 12 Simple Sets | 57 |

Chapter 13 The Priority Method | 60 |

Chapter 14 The Splitting Theorem | 66 |

Chapter 15 Maximal Sets | 72 |

Chapter 16 Infinite Injury | 83 |

Chapter 17 Index Sets | 93 |

Chapter 8 Incomparable Degrees | 39 |

Chapter 9 Upper and Lower Bounds | 43 |

Chapter 18 Branching Degrees | 99 |

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### Common terms and phrases

active at step active n-requirement Alg(N,N algorithm argument k choose closed set cofinite coinfinite RE set Comp construction Corollary created at step cursive describe step dg F dg G dg H dg Wr effective at step F and G F is recursive finite object finite set function F Hence I-minimal I-split inactive at step induction hypothesis infinite sequence insure Isomorphism Isomorphism Theorem Ix(a Lemma Let F maximal set n-holds n-re n-requirement with argument n-string n-tuple number in row oracle Parameter Theorem partial function permanent n-requirement piecewise recursive Post's Theorem prove quirement recursive function recursive in H recursive relation recursive set relativized requirement result set of degrees simple set smallest number Sn(i Splitting Theorem subtree suffices to show sufficiently large suppose temporary n-requirements tion undefined upper bound x e Wr