## Provability, Computability and ReflectionProvability, Computability and Reflection |

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### Contents

Chapter 2 Models of set theory | 177 |

Chapter 3 On the independence of the wellordering theorem from the ordering principle | 290 |

Chapter 4 On definable sets of positive integers | 339 |

Chapter 5 The classical and the ωcomplete arithmetic | 371 |

Chapter 6 Formal system of analysis based on an infinitistic rule of proof | 390 |

Chapter 7 An exposition of forcing | 416 |

Chapter 8 Some impredicative definitions in the axiomatic settheory | 479 |

Chapter 9 Models of axiomatic theories admitting automorphisms | 494 |

Chapter 10 On ωmodels which are not βmodels | 513 |

Chapter 11 Observations concerning elementary extensions of ωmodels I | 524 |

Chapter 12 An undecidable arithmetical statement | 531 |

Chapter 13 On extendability of models of ZF set theory to the models of KelleyMorse theory of classes | 553 |

### Common terms and phrases

6-model arbitrary arithmetic atomic formulae automorphisms axiom of choice axiom of constructibility axiomatic belongs calculus called cardinal computable functions consider consistent constant contains continuum hypothesis decision problem defined definition denote denumerable elementarily equivalent elements equation equivalent exists formal formula F Fr(F free variables function f Fundamenta Mathematicae Hence implies inductive assumption infer infinite infinitistic interpretation intuitionistic logic isomorphic Journal of Symbolic Kleene language lecture lemma limit number mapping Math maximal filter method model of ZF model theory Mostowski notion obtain ordinal number pair paper predicate primitive recursive function propositional function provable proved quantifiers recursively enumerable sets relation satisfies the condition semantics sentences set theory set-theoretical sets of integers subsets Symbolic Logic Tarski tion transfinite true undecidability valid well-ordering