Mathematical logic

Contents......Page 4
Preface......Page 6
Introduction......Page 8
1. Sets and words......Page 14
2. The language of the propositional calculus......Page 20
3. Axiom system and rules of inference......Page 24
4. The equivalence of formulas......Page 31
5. Normal forms......Page 34
6. Semantics of the propositional calculus......Page 42
7. Characterization of provable formulas......Page 47
8. Hilbertian propositional calculus......Page 51
9. Conservative extension of calculi......Page 55
10. Predicates and mappings......Page 64
11. Partially ordered sets......Page 69
12. Filters of Boolean algebra......Page 77
13. The power of a set......Page 81
14. The axiom of choice......Page 89
15. Algebraic systems......Page 95
16. Formulas of the signature Σ......Page 101
17. Compactness theorem......Page 109
18. Axioms and rules of inference......Page 116
19. The equivalence of formulas......Page 125
20. Normal forms......Page 129
21. Theorem on the existence of a model......Page 131
22. Hilbertian calculus of predicates......Page 138
23. Pure calculus of predicates......Page 143
24. Elementary equivalence......Page 148
25. Axiomatizable classes......Page 156
26. Skolem functions......Page 164
27. Mechanism of compatibility......Page 167
28. Countable homogeneity and universality......Page 180
29. Categoricity......Page 187
30. The Gentzen system G......Page 197
31. The invertibility of rules......Page 203
32. Comparison of the calculi CP^Σ and G......Page 209
33. Herbrand theorem......Page 216
34. The calculi of resolvents......Page 227
35. Normal algorithms and Turing machines......Page 235
36. Recursive functions......Page 246
37. Recursively enumerable predicates......Page 263
38. Undecidability of the calculus of predicates and Goedel's incompleteness theorem......Page 275
List of Symbols......Page 291
Subject Index......Page 294