## Mathematical logic |

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### Contents

The Nature of Mathematical Logic | 1 |

FirstOrder Theories | 9 |

Theorems in FirstOrder Theories | 26 |

Copyright | |

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### Common terms and phrases

A V B axiom of constructibility axiom system benign calculable Card(x cardinal closed formula conservative extension consistency proof constructible continuum hypothesis corollary countable decision method defining axiom disjunction element elementarily equivalent elementary extension equality axioms equality theorem equivalent explicit definition expression numbers extension by definitions F is defined F is recursive finitary follows function F function or predicate function symbol functions and predicates Hence Higman homomorphism hyperarithmetical identity axioms implies induction hypothesis infinite interpretation introduce isomorphism Lemma means n-ary function n-type natural numbers negation nonlogical axioms nonlogical symbols obtain ordinal partial functional predicate symbol prenex form provable prove Q(xu quantifiers recursive function recursive partial functional recursively enumerable set relation replace result special constants strongly undecidable structure subgroup subset suppose syntactical variables tautological consequence tautology theorem theory transfinite induction truth values unary predicate valid variable-free