Book:Peter B. Andrews/An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof

Subject Matter

 * Mathematical Logic
 * Type Theory

Contents

 * Preface
 * Introduction
 * Chapter 1 Propositional Calculus
 * 10. Formation Rules for $\mathscr P$
 * 10A. Supplement on Induction
 * 11. The Axiomatic Structure of $\mathscr P$
 * 12. Semantics, Consistency, and Completeness of $\mathscr P$
 * 13. Independence
 * 14. Propositional Connectives
 * 15. Compactness
 * 16. Ground Resolution
 * Chapter 2 First-Order Logic
 * 20. Formation Rules for the System $\mathscr F$
 * 21. The Axiomatic Structure of $\mathscr F$
 * 22. Prenex Normal Form
 * 23. Semantics of $\mathscr F$
 * 24. Independence
 * 25. Abstract Consistency and Completeness
 * 25A. Supplement: Simplified Completeness Proof
 * 26. Equality
 * Chapter 3 Provability and Refutability
 * 30. Natural Deduction
 * 31. Gentzen's Theorem
 * 32. Semantic Tableaux
 * 33. Skolemization
 * 34. Refutations of Universal Sentences
 * 35. Herbrand's Theorem
 * 36. Unification
 * Chapter 4 Further Topics in First-Order Logic
 * 40. Duality
 * 41. Craig's Interpolation Theorem
 * 42. Beth's Definability Theorem
 * Chapter 5 Type Theory
 * 50. Introduction
 * 51. The Primitive Basis of $\mathcal Q_0$
 * 52. Elementary Logic in $\mathcal Q_0$
 * 53. Equality and Descriptions
 * 54. Semantics of $\mathcal Q_0$
 * 55. Completeness of $\mathcal Q_0$
 * Chapter 6 Formalized Number Theory
 * 60. Cardinal Numbers and the Axiom of Infinity
 * 61. Peano's Postulates
 * 62. Order
 * 63. Minimization
 * 64. Recursive Functions
 * 65. Primitive Recursive Functions and Relations
 * Chapter 7 Incompleteness and Undecidability
 * 70. Gödel Numbering
 * 71. Gödel's Incompleteness Theorems
 * 72. Essential Incompleteness
 * 73. Undecidability and Undefinability
 * 74. Epilogue
 * Appendix Summary of Theorems
 * Bibliography
 * Index