.

0 (hodnocen0 x )

BK

Princeton : Princeton University Press, 1996

ix,378 s.

ISBN 0-691-02906-7 (brož.)

Princeton landmarks in mathematics and physics

Obsahuje předmluvu, úvod, rejstříky, údaje o autorovi

Logika matematická - učebnice vysokošk.

000005072

Contents // PREFACE ... v // INTRODUCTION ... 1 // 00. Logic ... 1 // 01. Names ... 3 // 02. Constants and variables ... 9 // 03. Functions ... 15 // 04. Propositions and propositional functions ... 23 // 05. Improper symbols, connectives ... 31 // 06. Operators, quantifiers ... 39 // 07. The logistic method ... 47 // 08. Syntax ... 58 // 09. Semantics ... 64 // CHAPTER 1. The Propositional Calculus ... 69 // 10. The primitive basis of ... 69 // 11. Definitions ... 74 // 12. Theorems of Pi ... 81 // Exercises 12 ... 85 // 13. The deduction theorem ... 86 // 14. Some further theorems and metatheorems of Pi ... 91 // Exercises 14 ... 93 // 15. Tautologies, the decision problem ... 94 // Exercises 15 ... 102 // 16. Duality ...106 // 17. Consistency ...108 // 18. Completeness ...109 // Exercises 18 ...Ill // 19. Independence ...112 // Exercises 19 ...115 // CHAPTER 11. The Propositional Calculus (Continued) ...119 // 20. The primitive basis of P2 ... 119 // 21. The deduction theorem for ...120 // Z // TABLE OF CONTENTS // • • • // V111 // 22. Some further theorems and metatheorems of ...121 // 23. Relationship of P2 to Pi ...125 // Exercises 23 ...128 // 24. Primitive connectives for the propositional calculus ...129 // Exercises 24 ...134 // 25. Other formulations of the propositional calculus ...136 // Exercises 25 ...138 // 26. Partial systems of propositional calculus ...140 // Exercises 26 ...143 // 27. Formulations employing axiom schemata ...148 // 28. Extended propositional calculus and protothetic ...151

// Exercises 28 ...154 // 29. Historical notes ...155 // Exercises 29 ...166 // CHAPTER III. Functional Calculi of First Order ...168 // 30. The primitive basis of F1 ...169 // Exercises 30 ...176 // 31. Propositional calculus ...178 // 32. Consistency of F1 ...180 // 33. Some theorem schemata of F1 ...186 // 34. Substitutivity of equivalence ...189 // Exercises 34 ...191 // 35. Derived rules of substitution ...191 // Exercises 35 ...195 // 36. The deduction theorem ...196 // 37. Duality ...201 // 38. Some further theorem schemata ...205 // Exercises 38 ... 206 // 39. Prenex normal form ...209 // Exercises 39 ...212 // CHAPTER IV. The Pure Functional Calculus of First Order . . 218 // 40. An alternative formulation ...218 // Exercises 40 ... 220 // 41. Independence ... 220 // Exercises 41 ...223 // 42. Skolem normal form ...224 // 43. Validity and satisfiability ...227 // Exercises 43 ... 231 // TABLE OF CONTENTS // ix // 44. Godefs completeness theorem ...233 // 45. Lowenheim’s theorem and Skolem’s generalization ...238 // Exercises 45 ...245 // 46. The decision problem, solution in special cases ...246 // Exercises 46 ... 257 // 47. Reductions of the decision problem ...270 // Exercises 47 ... 280 // 48. Functional calculus of first order with equality ...280 // Exercises 48 ... 282 // 49. Historical notes ...288 // CHAPTER V. Functional Calculi of Second Order ...295 // 50. The primitive basis of ...295 // 51. Propositional calculus and laws of quantifiers ...297 // 52. Equality ...300 // Exercises 52 ...302 //

53. Consistency of ...306 // 54. Henkin’s completeness theorem ...307 // Exercises 54 ...315 // 55. Postulate theory ...317 // Exercises 55 ... 333 // 56. Well-ordering of the individuals ...341 // Exercises 56 ... 342 // 57. Axiom of infinity ...342 // Exercises 57 ... 345 // 58. The predicative and ramified functional calculi of second order 346 // Exercises 58 ... 354 // 59. Axioms of reducibility ...354 // Exercises 59 ... 356 // INDEX OF DEFINITIONS ...357 // INDEX OF AUTHORS CITED ...373 // ERRATA ...377