Rockingham G.R. — Deducibility and Decidability :: Электронная библиотека попечительского совета мехмата МГУ

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Rockingham G.R. — Deducibility and Decidability

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Название: Deducibility and Decidability

Автор: Rockingham G.R.

Аннотация:

The classic results obtained by Gödel, Tarski, Kleene, and Church in the early thirties are the finest flowers of symbolic logic. They are of fundamental importance to those investigations of the foundations of mathematics via the concept of a formal system that were inaugurated by Frege, and of obvious significance to the mathematical disciplines, such as computability theory, that developed from them.

Derived from courses taught by the author over several years, this new exposition presents all of the results with their original proofs and central concepts in a manner that is unified by a systematic grounding of the notion of effectiveness in the semantics of the existential quantifier. Logicians and non-mathematicians, repelled by detail which is not obviously relevant in the standard textbooks, will be able to reach the heart of the matter with a minimum of fuss.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1990

Количество страниц: 162

Добавлена в каталог: 05.04.2008

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Предметный указатель

Logistic system, Church on      66—67
Lucas, J.R., alluded to      105
M      8 137 142
Machine, computing      42 70
Markov, A.A.      42
Martin, R.L.      82
Mates, B.      118
Matrix of a predicate-form      139
Matrix of numbers      52
Member      135
Mendelson, E.      21
Metamathematic/s, metamathematical      101 108
Model      142 148
Model of $\mathbf{P}$       98
Model of $\mathbf{Q}$       20—22
Model of $\mathbf{S}$       5
Model of $\mathbf{S}^{+}$       6
Montague's Fixed-point Lemma      85 88
Montague's fixed-point, M      85
Montague, mont      85 87—88
Montague, R.L.      79 84—88 128
Mostowski's Speed-up Theorem      93 fn. 122
Mostowski, A.      15 22 93 116 117 124 128—129
Mycielski, J.      122
Nelson, E.      22
ngn      64
Numeral      53 81
Numeralwise express      116
Oedipus      76
Operation      44—48 136
Order-type      96 fn.
Ordinal number      6 96
Papadimitriou, C.H.      39
Paradox/es of induction      4
Paradox/es of the Knower      79
Paradox/es, Liar paradox      77 79 109
Paradox/es, semantical paradoxes      73 76—80 94 110
Parikh, R.      98 123
Paris, J.B.      95 96
Parsons, C.      35
Part      53
Part, Pt, pt      54
Peano's Arithmetic      see “ $\mathbf{P}$ ”
Peano, G.      15
Perception — in connection with Goedel      102
Perception — in connection with Goedel and with Hilbert      104
Poincare, J.H.      20 78
Point      28 122—123 143
Post, E.L.      40 42
Prdfm      68
Predicate      134
Predicate, $\Delta$ -representable predicate      44
Predicate, $\Sigma$ -representable predicate      40 128
Predicate, Berry's predicate      4
Predicate, Cantor's diagonal predicate      10
Predicate, confirmable predicate      40
Predicate, decidable predicate      44—45 69 128
Predicate, diagonalization of a predicate      73
Predicate, extension of a predicate      see “Extension”
Predicate, meaning of a predicate      105 106 114—115
Predicate, range of significance of a predicate      77—78
Predicate, recursively defined predicate      49—58
Predicate, representable predicate      9—10
Predicate, second-level predicate      77 87
Predicate, sense of a predicate      105 106 114—115
Predicate, structural description of a predicate      80
Predicate, universal-predicate      139
Predicate, “determinacy” of predicates      3—4 103
Predicate-form      139
Predicate-form of type ((i), i)      87 112
Predicate-form, $\Delta$ -predicate-form, $\Sigma$ -predicate-form      23
Predicate-letter      see “Letter/s”
Predicative      77—78
Prefix      139
Prefix, px      84
Prior, A.N.      79 109 127—128
Procedure, confirmation procedure      38—39 43—44 69 72
Procedure, decision procedure      44
Procedure, disconfirmation      44
Procedure, effective procedure      13 14 27—36 37—38 49 84 101 117 119 121 132 148 149
Proof-theory      see “Tableau/x” “Regular” “Hilbert's
Property: $\vee$ -property, $\exists$ -property, $\forall$ -property      17—19 22 90 93 98
Pt, pt      54
Pudlak, P.      130
punctuation marks      136
Putnam, H.      131—132
Quantifi/cation, quantifiers: bounded quantifiers      2
Quantifi/cation, quantifiers: formal quantifiers      2 136
Quantifi/cation, quantifiers: informal      6 50—51
Quine, W.V.O.      1 fn. 51 76
quotation      73—75 79—82 137
Quotation, $\ulcorner \urcorner$       1
R      11
Rabin's Theorem      131
Rabin, M.O.      131
Range of a relation      135
Range of significance      see “Predicate”
Rdbl      93 105
Rddn      93
Reading      139—140
Recursion equation      87
Recursion theorem      87 95 112 137
Recursive, recursiveness      46—58 80 “Predicate”)
Reducibility      129—130
Relation      135
Relation, effective, effectively enumerable, relation      44—46
Relation, elementary relation      56—57 70 124 128
Relation, recursive, recursively enumerable, relation      46—48 116 124
Relation, total relation      121
Relevan/t      148
Relevance Principle      142 149
Remus, Uncle      4
Repleteness      27
Represent/ation, $\Sigma$ -represent      40 43 98—99
Represent/ation, goodness of a represent      105 106
Represent/ation, representability      8—10
Represent/ation, second-order represent      112 114
Represent/ation, “adequate” representation      114
Represent/ation, “canonical” representation      106 fn.
Rgcl      71
Rgtb      68 105
Richard, J.      82
Rimbaud, A. quoted      78
Ritchie, R.W.      56
Robinson's Arithmetic      see “ $\mathbf{Q}$ ”
Robinson, R.M.      15 22 116 117
Rogers, H.      43

Rosser's Theorem      99
Rosser, J.B.      93 116
Russell, B.A.W.      4 51 77—78 113 118 134
Ryle, G.      7 75 77
Ryll-Nardjewski's Theorem      131
Ryll-Nardjewski, C.      131
s-diagonalization      80
Satisfaction: formal      113
Satisfaction: informal      135
Saying & self-saying      76—78 109
Sbjfm      67
Schwabhauser, W.      21
Scott, D.      141
Second-level      see “Predicate” “Subject”
Second-order      see “”Logic
Self-reference      83—84
Self-saying      see “Saying”
Sentence      134
Sentence-form      137—138
Sentence-form of type B      11 63—64
Sentence-form of type R      11
Sentence-form, $\Delta$ -sentence-form      23
Sentence-form, $\Delta_{n}$ -sentence-form      124
Sentence-form, $\Pi_{n}$ -sentence-form      124
Sentence-form, $\Pi_{n}^{\bullet}$ -sentence-form      132
Sentence-form, $\Sigma$ -sentence-form      23
Sentence-form, $\Sigma_{n}$ -sentence-form      124
Sentence-form, $\Sigma_{n}^{\bullet}$ -sentence-form      132
Sentence-form, degree of a sentence-form      13 32
Sentence-form, descendance-chain for a sentence-form      13
Sentence-form, descendants of a sentence-form      13
Sentence-form, grounded sentence-form      13 124—128
Sentence-form, Imdsc      106
Sentence-form, immediate descendants of a sentence-form      12
Sentence-form, indices of a sentence-form      12
Sentence-form, simple sentence-form      64
Sentence-form, Typ      106
Sentence-form, type of a sentence-form      12
Sentence-letter      see “Letter/s”
SEQUENCE      136
Sequence, $\langle \ \rangle$       136
Sequent, numerical      52 57 62 65
Sequent, syntactical      59—60 62 65
Set      135
Set, empty set, $\emptyset$       6 145
Set, recursively enumerable sets      69—70
Set, union of sets, $\smile$       6 145
Set, universal set      140
Set, { }      6 755 145
Sheard, M.      112 fn.
Shepherdson, J.C.      22
Shoenfield, J.R.      148
simplicity      113
SIZE      53
Size, sz      54
Smullyan, R.M.      11 16 36 46 54 72 143—144
Sntfm      68
Sound/ness      5 14 18—19 148—149
Sound/ness of $\mathbf{P}$ assumed      89—90
St Paul      109
Standard/ly      see “Assign/ment” “Dictionary “Fit” “Model”
Standard/ly, | |      140 142
Standardization      41
Stating      see “Saying”
Stockmeyer, L.J.      39
Structural-descript/ion, structural-descriptive      80
Subject      77 134
Subject, second-level subject      77—78
Subject-form      66 137—138
Subject-form, $\Delta$ -, $\Sigma$ -subject-form      23
Subject-letter      see “Letter/s”
Survey able      14
Symbolic logic, Church on systems of logic      66—67
Syntax      65—66
Systematic extensions, systematically generated chains      27—32
Systematic, Procedure      27—36 37 38 42 69 70 72
sz      54
t      see “Convention T”
Tableau/x, $\Pi$ -tableau/x      125
Tableau/x, $\Sigma tb$       68
Tableau/x, $\Sigma$ -tableau/x      24—26 27—32 46 71 125
Tableau/x, Clrgtb      71
Tableau/x, regular tableau/x      24 143—145
Tableau/x, semantic tableau/x      143
Takeuti, G.      97 106 114
Tarski's theorem      109 110 111 115 127
Tarski, A.      5 18 21 22 60 66 107 109 110 111—115 116 117 127 137 148
Term      136
tpfm      69
Transitiv/e, transitivity      1 5 6
Translat/e, translation      20
Translat/e, translation, formal translate      21 132 147
Truth of      135
Truth of, being true of oneself      75 f.
Truth, Carnap on truth      65—66
Truth, constructive truth      35—36 110
Truth, decidability of truth      118—119
Truth, distinguished from being standardly assigned T      142
Truth, Tarski's “definition” of truth      111—115 137
Tuple      see “Sequence”
Turing machine      101
Turing, A.M.      40 42 54
Typ      106
TYPE      see “Sentence-form” “Predicate-form”
union      135
Union, $\smile$       6 145
Universal computing machine      42 70
Universal-form      21 147
Universal-predicate      139
Universal-procedure      42 70
Universal-set      149
Universe      140
Value      135
van Heijenoort, J.      67
Variables      66 136—137
Variant      140
von Neumann, J.      91 119 120
Waismann, F.      103
Webb, J.G., alluded to      105
Well-ordering      10 66 96—97 137
Wittgenstein, L.J.J.      7 14 41 67 77 78 97 103 105 118—119
Wright, C.J.      4 39 102
Zermelo, E.      110
“Determinacy” of predicates      3—4 103
“Order of precedence”      96 fn.
“Rogue” form, the      5 19—22
“Rogue” form, the, cf.      31

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