Gentzen G. — The collected papers of Gerhard Gentzen :: Электронная библиотека попечительского совета мехмата МГУ

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Gentzen G. — The collected papers of Gerhard Gentzen

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Название: The collected papers of Gerhard Gentzen

Автор: Gentzen G.

Аннотация:

Gerhard Gentzen was born in Greifswald, Pomerania, on November 24th, 1909. He spent his childhood in Bergen on the Isle of Riigen in the Baltic Sea.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 338

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Definite object      54 111
Definite predicate      54 141
Definite proposition      142
Definition      14 156 160
Definition of the objects of proof theory      194 211
Definition table      158
Definition tables and decision rules      161
Degree of a CJ-inference figure      257
Degree of a cut      256
Degree of a derivation      89
Degree of a formula      15 71 254
Degree of a sentence      43
Degree of an induction proposition      311
Delimitation of the forms of inference in proof theory      138 228
Denton, J.      6
Denumerability      29 200 223 229 241—243 246 247
Denumerability and algebra      223
Denumerability and Skolem's theorem      241
Dependent formula      76
Dependent formulae and propositions      76 150 152
Derivability and logical consequence      2 3 24 33
Derivability of a contradiction      112
Derivable formula      55 112
Derivable formula in arithmetic      55 112
Derivation      55 72 74 151 179 216 257 258 287 309 cf.
Derivation in the ordinary sense      291
Derivation in tree form      73 258
Derivations in tree form      73 258
Derived concept      57 139 144 155—157 160 193
Derived concepts in elementary number theory      155—157
Description operator      cf. "The ... such that"
Difficulties involved in consistency proofs      229 seq.
Direct proof      165
Disjunction      70 77 cf.
Disputable forms of inference      158 170 197 261
Distinction of cases      78 153 254 cf.
Dots      54
Dreben, B.      6
Dual(ity)      86 137 138 259
Duality of LK      86 259
e      77
Eigenvariable      77 84 255
Elementary formula      54 71 cf. "Prime
Elementary inference      145
Elementary number theory      3 8 68 132 136—138 154 197 198 223 239 250 287 292 309
Elementary number theory and bound predicate variables      297
Elementary number theory and transfinite induction      292 307
Eliminability of negation      66 67 81
Eliminability of the cut      15 28
Elimination of double negation      81 153 168—170 181 204 259
Elimination of logical connectives      5 80 82 148 150 168 258 259 262 263 269 293
Elimination of the double negation      168—170
Elimination Theorem      cf. "Hauptsatz"
Empty antecedent      72
Empty antecendent      72
Empty endsequent      261
Empty endsequent and consistency      261
Empty sequent      16 72 103 255 261
Empty succedent      72 82 112
End formula      73
Endformula      55 73 151
ending      264 300
Endsequent      6 257
Endsequent after the reduction step      181
Endsequent and the subformula property      6
Equality      110 111 216 309
EQUIVALENCE      70
Equivalence between formulae and sequents      115
Equivalence of classical calculi      128 seq.
Equivalence of derivations      116
Equivalence of formulae      73 115
Equivalence of intuitionist calculi      116 seq.
Equivalence of logical calculi      69 115 116 128 131
Equivalence of net elements      49
Equivalence of sequents      115
Equivalence of the classical calculi      128 seq.
Equivalence of the intuitionist calculi      116 seq.
Euclid      5 144 145 148—150 155 170 248
Evaluation of terms      159
Examples, arithmetic axiom formulae      56 57 111 112 114 115
Examples, axioms of elementary number theory      157
Examples, basic logical sequents      180
Examples, basic mathematical sequent      260
Examples, basic sequents      86 257
Examples, circulus vitiosus in analysis      134
Examples, contradiction      262
Examples, degrees of formulae      254
Examples, derivations      258 260
Examples, forms of inference      148
Examples, formulae      54 141 215 253
Examples, inference figure      257
Examples, LJ-derivation      85
Examples, LK-derivation      85
Examples, mix      89
Examples, natural deductions      74 75
Examples, natural sum      296 297
Examples, NJ-derivations      79 80
Examples, ordinal numbers      187
Examples, prime formula      253
Examples, proof      144
Examples, reduction rule      176
Examples, sentence system without an independent axiom system      40
Examples, sequent      255
Examples, subformula property      88
Examples, subformulae      71
Examples, terms      54 141
Examples, theorem in proof theory      137
Examples, true formulae      74
Examples, true numerical propositions      114
Excluded Middle      cf. "Law of the excluded middle"
Existence      246 248—250
Existential proposition      201 226
Existential quantifier      4 54 70 77 cf. "
Expression      53 54 70 211
Extended Hauptsatz      cf. "Sharpened Hauptsatz"
Extension of a formalism      17 114
Extension of the reduction procedure      17 198
False formula      79 114
False sequent      254 269
Falsity      cf. "Truth"
Fan Theorem      8 26
Fermat's last theorem      161
Fermat's last theorem and provability      166
Fermat's last theorem and the decidability of the predicate calculus      239
Fermat's last theorem and the existence of a decision rule      161
Fermat's last theorem and the reduction rule      176
Fermat, P.      161 162 166 176 239
figure      70 72
Finite mathematics      158 seq.
Finite sentence system      39
Finite sets of natural numbers      142 143
Finiteness of the reduction procedure      186 191 193
Finitist      10 18 169 227 250
Finitist forms of inference      135
Finitist interpretation and the statability of a reduction rule      173 201 206
Finitist interpretation of $\forall, &, \exists, \vee$       163—165 169
Finitist interpretation of $\supset, \neg$       167—170
Finitist interpretation of complete induction      166
Finitist interpretation of Fermat's last theorem      166
Finitist interpretation of number-theoretical axioms      164
Finitist meaning of $\rightarrow$       206
Finitist nature of transfinite ordinal numbers      277 278 285
Finitist sense of actualist propositions      201
Finitist sense of transfinite propositions      162
Finitist techniques of proof      171 193 194 210 212 238 239
Finsler, P.      315
Fitch, F.B.      12 13 27
follows      212
Formal arithmetic in LK      110 seq.
Formal system      68 233

Formalization of elementary number theory      138 139 252
Formalization of logical deduction      68
Formalization of logical deductions      68
Formalization of proofs      137 138 228 258
Formalization of propositions      69 70 139 140
Formalization of techniques of proof      139 143
Formalization of the forms of inference      149 seq.
Formalization of the forms of inference in elementary number theory      149 seq.
Formalization of transfinite induction      291
Formalized arithmetic      55
Formally identical S-formulae      72
Forms of inference      30 138 139 144 228
Forms of inference and axiom systems      238
Forms of inference and decision procedures      161 seq.
Forms of inference and restricted transfinite induction      17 308
Forms of inference for sequents      150 151 255 256
Forms of inference in elementary number theory      148 149
Formula      54 70 140 141 214 253 289 314
Formulae and propositions      140 141
Formulae and sequents      72
Four-colour problem      223
Fractions      142
Fraenkel, A.      28 240 314
Free choice sequence      245 246
Free variable      55 141 144 215 288
Frege, G.      4 24 68
Function      69 110 156 158 160 174 194 198 199 211 245 246 260 287 288
Function symbol      140 141 288
Functions in elementary number theory      143 156
Functions in New      253 288
Fundamental conjecture      15
Fundamental principle of constructivism      225 235 247
Fundamental principle of constructivism and classical analysis      247 250
Fundamental principle of intuitionism and the actualist interpretation      235
Fundamental principle of proof theory      162
Fundamental theorem of algebra      236
G      293
Gauss, C.F.      225
General set theory      3 224 240 cf.
Gentzen's fundamental principle      162
Gentzen, G.      vi vii viii 1—28 201 314 316 317
Geometry and infinity      224
GLC      13 14
Glivenko, V.      x 116 314
Goedel numbers (correlation of natural numbers)      197
Goedel's equivalence theorem      169
Goedel's theorem      4 11 16 17 25 67 138 193 197 238 242 287
Goedel's theorem and consistency proofs      197 229 232 233 236 238—240 284 287
Goedel's theorem and constructivist techniques of proof      239
Goedel's theorem and Incompleteness      233 238 240 308
Goedel's theorem and restricted transfinite induction      16 232 284
Goedel's theorem and Skolem's theorem      242
Goedel's theorem and the consistency of arithmetic      67
Goedel's theorem and the reduction rule      213
Goedel's theorem on completeness      240
Goedel's theorem on decidability      239
Goedel, K.      xi 3 4 7 8 11 15—18 24 25 67 138 169 193 197 199 212 213 215 229 232 233 236 238—240 242 287 308 313—317
Goldbach's conjecture      140 161
Goldbach's conjecture and decidability      161 168
Goldbach, C.      140 161
Goodstein, R.L.      26
Hauptsatz      5—7 15 68 69 83 85 87 88 317 cf.
Hauptsatz and intuitionist propositional logic      103
Hauptsatz and the cut      5
Hauptsatz and the decision rule      69
Herbrand theorem      6 313
Herbrand — Gentzen theorem      7 313 cf.
Herbrand, J.      6—8 13 25 56 236 313 314
Hertz, P.      ix 1 2 29 31 32 40 312
Hessenberg, G.      317
Heyting, A.      3 56 58 61 65 68 69 75 81 106 117 236 249 313 315 316
Hilbert's finitist point of view      4 9 10 22 23 67 222 237
Hilbert's Programme      3 4 8 18 135 214 222 227 236 238
Hilbert's programme and philosophy      237
Hilbert, D.      vii x 3 4 6 8 9 13 14 16 18—22 24 26—28 53 54 56 57 61 65 67 68 69 73—75 81 86 103 104 114—117 135 165 214 216 222
Hilbert, D. and Ackermann, W.      14 24 27 53 54 56 57 61 65 68 74 86 103 104 114 117 214 313—315
Hilbert, D. and Bernays, P.      6 9 26 27 315 317
Hjelmslev, J.      18 28 316
i      77
IA      83
Ideal element      18 247 250
Ideal point      247 248 250
Ideal proposition      247
Idealism      19 cf.
Idealization of reality      23 248
Immediate inference      31 cf.
Implication      10 70 77 cf.
Impredicative definition      14
Incompleteness and calculation procedures      245
Incompleteness and consistency proofs      17 198
Incompleteness and Goedel's theorem      233 238 240 308
Incompleteness and restricted transfinite induction      16 17
Incompleteness and the axiomatic method      17
Incompleteness and the reduction procedure      17
Incompleteness of elementary number theory      307 308
Incompleteness of formal systems      7 143 198 233 307
Indefinite number      cf. "Term"
Indefinite proposition      140 142
Independent axiom system      2 39
Independent sentence system      39
Indeterminate      314
Indirect existence proof      226 235
Indirect existence proofs      226 235
Indirect existence proofs and the antinomies of set theory      235
Indirect proof      169 250 cf.
Indisputable forms of inference      158 171 193 197 200 228 229
Indisputable forms of inference and consistency proofs      200
Indisputable forms of inference and the constructivist point of view      228 250
Indisputable forms of inference and the proof of finiteness      197
Indisputable forms of inference and the reduction procedure      197
Indisputable forms of inference of elementary number theory      158
Induction      cf. also "Complete induction" "Transfinite
Induction axiom      309
Induction proposition      145
Induction step      145
Inference      69
Inference figure      72 73 82 83 249 289
Inference figure schema      77 83 84 117 125 129 255 256 290 291
Inferences in Euclid's proof      145 seq.
Infinite domain of objects      222
Infinite sentence system      29 40
Infinite sets of objects      142 224
infinity      3 223 234 237
Infinity and geometry      224
Infinity and the antinomies of set theory      234
Informal arithmetic      55
Informal completeness of the forms of inference      34
Informal correctness of the forms of inference      33
Informal sense of a formula      141
Initial formula      73 74 76
Initial sentence      35
Initial sequent      83
Insufficiency of the natural numbers as ordinal numbers in proof theory      232
INTEGER      142
Interchange      84 129 151 256
Interchange in the antecedent      84 151
Interchange in the antecendent      84 151
Interchange in the succedent      84 129
Interdependence of the logical connectives      171
Introduction of logical connectives      5 80 82 148 150 168 258 262 263 269 293
Introduction of predicate symbols in logical calculi      111
Intuitionism fundamental principle of -      225 235
Intuitionist      3 10 135 169 227 235 250
Intuitionist analysis      18 244
Intuitionist and finitist uses of infinity      11
Intuitionist arithmetic      4 52 53 54 55
Intuitionist concepts as ideal elements      250
Intuitionist consistency of classical arithmetic      4
Intuitionist delimitation of the forms of inference      135 163
Intuitionist interpretation of infinity      235

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