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 $1986$, Academic Press

ISBN 978-0120585366.

Subject Matter

  • Mathematical Logic
  • Type Theory


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