## A Friendly Introduction to Mathematical LogicAt the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises. |

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### Contents

Structures and Languages | 1 |

Deductions | 41 |

Completeness and Compactness | 73 |

Incompleteness from Two Points of View | 103 |

Syntactic IncompletenessGroundwork | 117 |

The Incompleteness Theorems | 169 |

Computability Theory | 195 |

Summing Up Looking Ahead | 265 |

Just Enough Set Theory to Be Dangerous | 279 |

Solutions to Selected Exercises | 283 |

359 | |

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### Common terms and phrases

algorithm arity assignment function assume atomic formula binary function binary relation bit string Chaff Chapter clause computable set consistent set constant symbol construction sequence Corollary countable deduction define definition denote Diophantine equation element elementarily equivalent Entscheidungsproblem equation equivalent example Exercise existential exists finite first-order formal free variables function f Gödel number holds Incompleteness Theorem induction hypothesis infinite isomorphic L-formula L-structure language Lemma LNT-formula logical axioms mathematical n-ary natural numbers nonlogical axioms nonstandard Notice number of symbols Peano Arithmetic predicate primitive recursive function proof provable prove quantifier real numbers recursive set rule of inference Section semi-computable set set of axioms set of sentences Soundness Theorem statement structure subset Suppose Th(A ThmA total computable function true universe variable-free terms write