Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Preface xvii
4. Acknowledgments xix
5. Introduction xxi
6. I. Classical Propositional Logic 1
7. II. Abstracting and Axiomatizing Classical Propositional Logic 27
8. III. The Language of Predicate Logic 53
9. IV. The Semantics of Classical Predicate Logic 69
10. V. Substitutions and Equivalences 99
11. VI. Equality 113
12. VII. Examples of Formalization 121
13. VIII. Functions 139
14. IX. The Abstraction of Models 153
15. X. Axiomatizing Classical Predicate Logic 167
16. XI. The Number of Objects in the Universe of a Model 183
17. XII. Formalizing Group Theory 191
18. XIII. Linear Orderings 207
19. XIV. Second-Order Classical Predicate Logic 225
20. XV. The Natural Numbers 263
21. XVI. The Integers and Rationals 291
22. XVII. The Real Numbers 303
23. XVIII. One-Dimensional Geometry 331
24. XIX. Two-Dimensional Euclidean Geometry 363
25. XX. Translations within Classical Predicate Logic 403
26. XXI. Classical Predicate Logic with Non-Referring Names 413
27. XXII. The Liar Paradox 437
28. XXIII. On Mathematical Logic and Mathematics 461
29. Appendix: The Completeness of Classical Predicate Logic Proved by Gödel’s Method 465
30. Summary of Formal Systems 475
31. Bibliography 487
32. Index of Notation 495
33. Index 499