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Hilbert D., Ackermann W. — Principles of mathematical logic
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Название: Principles of mathematical logicАвторы: Hilbert D., Ackermann W. Аннотация: This translation of the Grundziige der Theoretischen Logik of Hilbert and Ackermann has been made from the second German edition, which was published in 1938 and has since enjoyed the status, assuredly well-merited, of a classic text in the field of mathematical logic. Those who have cooperated in the translation have sought both to give an exact English rendering of the sense and intent of the original text and also, so far as possible in a different language, to reproduce something of its manner and style. It has nevertheless been judged necessary to depart in some respects from the letter of the German text at places where, in the light of the general advance in precision of logical terminology since the text was written, its formulations now seem ambiguous or otherwise imperfect, and especially at places where technical criticism of the text itself has shown it to be in error. It is one of the purposes of this preface to call the reader's attention to these changes, for which the editor must assume responsibility.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1950Количество страниц: 185Добавлена в каталог: 29.08.2013Операции: Положить на полку |
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Aristotelian logic 48f Associative Law of conjunction and disjunction 7 Axiom of Choice 130 156 Axiom of extensionality 15 Axiom, systems of first and second order 107 Axioms of predicate calculus of order 155f Axioms of predicate calculus, completeness of 92f 130 Axioms of predicate calculus, independence of 87 Axioms of restricted predicate calculus 67f Axioms of second order predicate calculus 131 Calculus of classes 44 Calculus, functional 165 Calculus, predicate 44 165 Calculus, predicate, derivation of rules and formulas 71f Calculus, predicate, extended 125 Calculus, predicate, monadic 44 119 132 Calculus, predicate, of order 152 Calculus, predicate, of second order 125 Calculus, predicate, restricted 55 Calculus, sentential 3 165 Combinations of sentences, logically true 14 Combinations of sentences, simplification of 20 Combinations of sentences, totality of 18 Combinations of sentences, transformation of 12 Commutative Law of Sentential Calculus 7 Conjunction 7 Connectives, fundamental logical 3 Consistency, problem of 38 87f 111 158 Constants, individual 102 168 Constituents 19 Contradiction 167 Contradictory, construction of, in predicate calculus 80 Convergence, uniform and ordinary 64 Correspondence, one-to-one 142 Decision problem 112f 132 Decision Problem, reduction theorems in 118f Dedekind cut 158 Deduction of consequences of given axioms in predicate calculus 101f Deduction of consequences of given axioms in sentential calculus 23 Derivation of rules and formulas in predicate calculus 71f Disjunction 7 Dispensability of fundamental logical connectives 10 Distributive laws of sentential calculus 7 Domain of individuals 68 102 105 Dual 167 Duality Principle of predicate calculus 81f Duality Principle of sentential calculus 16 167 Either—or 4 Elimination problem in predicate calculus 132f Equivalence, set theoretic 142 Equivalences, sentential 5f Formula, definition of, in predicate calculus 65f Formula, satisfiable 113 129 Formula, universally valid 68 Formula, valid 68 129 German letters, use of 16 67 Greek letters, use of 102 Identity, predicate of 107 126 Implication 7 Individual constants 102 Individual variable 65 Individuals 57 Individuals, domain of 68 102 105 Induction, mathematical 126 Intersection 46 142 143 Italic letters, use of 65 Judgments, Particular 47 59 168 Judgments, universal 45 58 168 Least upper bound, theorem of 160 Level of a predicate 152f Logic, Aristotelian 48f Logic, traditional 48 55 Logical paradoxes 143f Negation, formation of, in sentential calculus 15 Normal form, conjunctive, in sentential calculus 12 17 Normal form, disjunctive, in sentential calculus 17 Normal form, distinguished conjunctive 19 Normal form, prenex 83 Normal form, Skolem 85 Number Concept, logical introduction of 136f Numerical equivalence of predicates 137 One-to-one correspondence 142 OR 4 Ordering of a set 143 Paradoxes, logical 143f Parentheses, elimination of 6 66 Particular Judgments 47 58 Pascal's theorem 108 Predicate 44 Predicate of second level 135 Predicate, level of 152 Prefix 84 Principia Mathematica 2 28 153 162 Product, logical 7 Proposition 165 168 Quantifier, existential 59 125 Quantifier, universal 58 125 Real numbers, foundation of theory of 158 Reduction theorems in the decision problem 118f Reflexivity 135 Rule for Universal and Existential Quantifiers 70 Rule of Implication 28 Rule of Interchange of Quantifiers 60 82 Rule of substitution 79 Rules for rewriting bound variables 70 Rules of elimination, of sentential calculus 20 Satisfiability, problem of 22 113 128 Scope of a quantifier 67 Sentential calculus, axioms of 27 Sentential calculus, axioms of, completeness of 42 Sentential calculus, axioms of, independence of 40 Sentential calculus, proof of rules and formulas in 30 Sequence of Natural Numbers, basic properties of 61 Set of all subsets 142 Set theory 139 Sets, ordered 143 Sets, well-ordered 143 Sheffer stroke 11 29 subclass 46 142 Sum, logical 7 Syllogisms 49 Symmetry 135 Tautology 167 Theory of types, simple and ramified 153 Traditional Logic 48 55 Transitivity 135 Truth function 5 Truth tables 166 union 46 142 143 Universal Judgment 45 58 Universal validity, problem of, in predicate calculus 112 128 Universal validity, problem of, in sentential calculus 21 Valid formulas 68 129 Variables, bound and free 59 Variables, individual 65 168 Variables, predicate 65 165 Variables, sentential 65 168 Well-ordering 143
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