## 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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Dislike the textbook. Not very helpful ways to approach the certain problems. There needs to be more examples in the book, so future students are able to learn better to solve problems. Never go for this textbook. Instead, go for the different logic textbook, like Mendelson's textbook, if you are taking Math Logic course.

### Contents

1 | |

11 | |

Chapter Two FirstOrder Logic | 67 |

Chapter Three Undecidability | 182 |

Chapter Four SecondOrder Logic | 282 |

307 | |

LIST OF SYMBOLS | 309 |

311 | |

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### Common terms and phrases

Assume atomic formulas axiom group axiomatizable theory binary relation Boolean function cardinality Cn A E compactness theorem computable consistent constant symbols COROLLARY countable decidable deduction definable deﬁned definition effectively enumerable elementarily equivalent example Exercise expression fact ﬁrst first-order first-order logic formal language function f function symbol GĻodel numbers Hence infinite isomorphic lemma logical axioms many-sorted modus ponens n-place function natural numbers notation number theory obtained occur free one-to-one parameters partial function PrbT PROOF quantifier-free quantifiers real numbers recursive function recursive partial function recursively enumerable register machine representable in Cn satisfiable satisﬁes second-order second-order logic Section 3.5 sentence symbols sentential logic set of sentences set theory Show soundness theorem structure suppose translated true truth assignment two-place predicate symbol universe valid variable Z-chains