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Hilbert D., Ackermann W. — Principles of mathematical logic
Hilbert D., Ackermann W. — Principles of mathematical logic

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Название: Principles of mathematical logic

Авторы: Hilbert D., Ackermann W.


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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1950

Количество страниц: 185

Добавлена в каталог: 29.08.2013

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Предметный указатель
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 $\omega$      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 $\omega$      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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