## Proof Theory: A Selection of Papers from the Leeds Proof Theory Programme 1990The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists. |

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### Contents

W POHLERS | 27 |

H SCHWICHTENBERG | 79 |

W BUCHHOLZ | 115 |

S BUSS | 149 |

E CICHON | 171 |

S FEFERMAN | 195 |

HOWE | 227 |

RATHJEN | 251 |

J TUCKER and J ZUCKER | 275 |

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additive apply arithmetic assume assumption atomic axioms BASIC bounded calculus called claim closed complexity computable consequence consider construct contains corresponding define definition denote derivation elements elimination equality equivalent example expression fact finite follows formal formula give given hence hierarchy holds immediate implies induction hypothesis inference interpretation introduce intuitionistic language least Lemma limit logic means multisets notations Note obtain occurring operator ordinal analysis path ordering predicate premise primitive recursive programs proof Proof Theory properties provably prove quantifiers rank recursive functions reflection relation replaced represents respectively restricted result RS(Q rule satisfying scheme semantics sequent sort standard step structure Suppose symbol termination Theorem theory tree true University usual variables write yields