## Introduction to Metamathematics |

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### Contents

THE THEORY OF SETS 1 Enumerable sets 2 Cantors diagonal method 3 Cardinal number | 3 |

4 The equivalence theorem finite and infinite sets | 11 |

Higher transfinite cardinals | 17 |

Copyright | |

83 other sections not shown

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### Common terms and phrases

additional applied arithmetic Axiom Schema axioms bound Chapter classical completely computable conclusion consider consistency constant constructed containing Corollary corresponding decision deduction defined definition depends distinct domain effectively entities enumerable equality equations equivalent establish EXAMPLE exists expressed extended finite formal system give given Gödel number Hence hold hypothesis induction inference infinite interpretation intuitionistic Lemma letter formula logical machine mathematics means metamathematical method natural numbers notion number-theoretic objects obtain occur operation partial recursive particular postulates predicate calculus predicate letter present primitive recursive problem procedure proof proposition proposition letter propositional calculus provable prove quantifiers realizes recursive function Remark replace representing respectively result rules satisfied sense sequence Similarly simply situation square step substitution Suppose symbols Theorem theory true variables VxA(x