Author(s): Gaisi Takeuti
Series: Studies in Logic and the Foundations of Mathematics 81
Edition: First Edition
Publisher: Elsevier Science
Year: 1975
Language: English
Pages: 361
Preface......Page 3
1. Formalization of statements......Page 4
2. Formal proofs and related concepts......Page 8
3. A formulation of intuitionistic predicate calculus......Page 18
4. Axiom systems......Page 20
5. The cut-elimination theorem......Page 21
6. Some consequences of the cut-elimination theorem......Page 28
7. The predicate calculus with equality......Page 38
8. The completeness theorem......Page 41
9. A formulation of Peano arithmetic......Page 67
10. The incompleteness theorem......Page 72
11. A discussion of ordinals from a finitist standpoint......Page 80
12. A consistency proof of PA......Page 96
13. Provable well-orderings......Page 114
14. An additional topic......Page 123
15. Second order predicate calculus......Page 126
16. Some systems of second order predicate calculus......Page 134
17. The theory of relativization......Page 145
18. Truth definition for first order arithmetic......Page 150
19. The interpretation of a system of second order arithmetic......Page 156
20. Simple type theory......Page 161
21. The cut elimination theorem for simple type theory......Page 167
4. Infinitary Logic......Page 180
22. Infinitary logic with homogeneous quantifiers......Page 183
23. Determinate logic......Page 211
24. A general theory of heterogeneous quantifiers......Page 242
25. Introduction......Page 277
26. Ordinal diagrams......Page 282
27. A consistency proof of second order arithmetic with the Π^1_1-comprehension axiom......Page 309
28. A consistency proof for a system with inductive definitions......Page 325
29. Provable well-orderings......Page 337
30. The Π^1_1-comprehension axiom and the ω-rule......Page 339
31. Reflection principles......Page 345
Index......Page 358
