Book:Peter B. Andrews/An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
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Peter B. Andrews: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
Published $\text {1986}$, Academic Press
- ISBN 978-0120585366
Subject Matter
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 $\QQ_0$
- 52. Elementary Logic in $\QQ_0$
- 53. Equality and Descriptions
- 54. Semantics of $\QQ_0$
- 55. Completeness of $\QQ_0$
- 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