## A mathematical introduction to logicA Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students |

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### Contents

Chapter One SENTENTIAL LOGIC | 14 |

Chapter Three UNDECIDABILITY | 174 |

Chapter Four SECONDORDER LOGIC | 268 |

Copyright | |

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### Common terms and phrases

asserts Assume atomic formulas axiom group axiomatizable theory binary binary relation Boolean function cardinality Cn AE compactness theorem computable connective symbols consistent constant symbol Corollary countable decidable deduction definable in 91 definition effectively enumerable elementarily equivalent English equality example Exercise expressions fact finite number finite sequence finite subset first-order logic formal language function g Godel number Hence inductive hypothesis infinite integers isomorphic Lemma logical axioms many-sorted modus ponens n-ary natural numbers notation number theory obtained occur free one-place one-to-one operation parameters partial function prenex procedure Proof quantifier quantifier-free real numbers recursive functions recursive partial function recursively enumerable register machine representable in Cn second-order second-order logic Section sentence symbols sentential logic set of Godel set of sentences set theory structure suppose tautologically equivalent translation true in 91 truth assignment two-place predicate symbol valid variable Z-chains