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

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Предметный указатель

#      279
$(\mathfrak{x})$       54
$fu_{1}$       289
$fu_{2}$       289
$\curlyvee$       70 218
$\curlywedge$       70 72 79 218
$\exists$       70 83 140 148 153 159 161 163 164 169 170 171 216 253 313
$\exists-E$       77 78 153
$\exists-I$       77 153
$\exists-IA$       84
$\forall$       4 24 70 83 140 148 161 163 169 216 313
$\forall-E$       77 152 203
$\forall-I$       77 78 152 183 188 190 203
$\forall-IS$       84
$\mathbf{E}$       54 61
$\mathcal{E}$       289
$\mathfrak{I}f$       95
$\mathfrak{M}$       90
$\mathfrak{S}$       46
$\mathfrak{S}^{b}(\mathfrak{S}^{x_{1}...x_{\nu}}_{q_{1}...q_{\nu}})$       58
$\mathfrak{S}_{q}$       108
$\mathfrak{T}$       46 48 50
$\neg$       54 70 77 83 140 148 149 153 168 181 206 253 313
$\neg-E$       77 78
$\neg-I$       77 79 183 188 190
$\omega$       230 seq. 278
$\omega_{\alpha}$       288
$\overline{\mathfrak{A}}$       42
$\overline{\mathfrak{S}}$       46 48
$\rightarrow$       70 71 201
$\supset$       54 70 83 140 148 149 153 167 169 171 206 253 290 313
$\supset-E$       77 153
$\supset-I$       77 78 153
$\supset\subset$       70 313
$\varepsilon_{0}$       11 12 16 17 233 284 285 287
$\vee$       54 61 70 78 83 140 148 149 152 163 165 169 171 253 254 313
$\vee-E$       77 78 152 181 293 cf.
$\vee-I$       77 152 293
$\vee-IA$       84
$\vee-IS$       84
&      54 70 83 140 148 153 163 164 169 181 253 313
&-E      77 152 181 203 293
&-I      77 152 203 293
&-IA      83 84
&-IS      83 84
Abandonment of the natural concept of a sequent      255
Absolute consistency      9 14 138 228 237
Accessible ordinal number      192 195
Ackermann function      156
Ackermann, W.      12 14—16 24 27 23 53 54 56 57 61 65 68 74 86 103 104 114 117 156 214 216 236 240 313—316
Actualist      19 cf.
Actualist concept of a function      245
Actualist concept of a set      134
Actualist interpretation and intuitionism      235
Actualist interpretation and Skolem's theorem      241
Actualist interpretation and the continuum      242
Actualist interpretation and the stability of a reduction rule      173
Actualist interpretation of classical analysis      243 seq.
Actualist interpretation of Fermat's last theorem      162
Actualist interpretation of infinity      18 224 235 247
Actualist interpretation of transfinite propositions      162
Actualist mathematics and constructivism      248 250
Actualist mathematics and existence      248
Actualist meaning of $\rightarrow$       206
Actualist sense of transfinite propositions      162
Adequacy of the definition of a formula      142
Adjunction      151 152 cf. "Assumption"
Algebra      2 200 223 236
Als ob      19 28 cf.
Alternative forms of complete induction      155
An sich      18 19 28 134 cf.
Analysis      3 65 134 137 143 197 199 200 223 235 242 250 296 309 316
Analysis and infinite sets of objects      142 224
Anderson, J.      25
Antecedent formula      151 254
Antecendent      2 30 71
Antecendent formula      151 254
Antinomies of set theory      3 23 132—136 158 162 224 227 228 234—237
Antinomies of set theory and indirect existence proofs      235
Antinomies of set theory and infinity      234
Antinomies of set theory and logicism      237
Antinomies of set theory and the natural numbers      133 136
Applications of the Hauptsatz      103 seq.
Applied mathematics      249
Argument      71
Arithmetic      3 8 53 55 110 136 cf.
Arithmetic without complete induction      69
As if      18—21 23 28 201 250 cf.
Assumption      150 164 165 254 cf.
Assumption formula      74—76
Assumption, calculus      5
Assumption, formula      74—76 82
Assumptions in proofs      150
Auxiliary calculus      128 seq.
Auxiliary concept of "satisfaction"      33
Auxiliary symbol      70 71 217
Axiom      55 68 69 136 144 151 194
Axiom formula      55 56 111 112 114 309
Axiom formulae for equality      309
Axiom formulae of arithmetic      56 57 111 112 114 115
Axiom formulae of intuitionist logic      56
Axiom of Choice      214 217 221
Axiom of comprehension      216 220
Axiom of infinity      12 13 214 222 240 241
Axiom of infinity and consistency proofs      222 240
Axiom of reducibility      13
Axiom of set formation      216
Axiom system      2 3 39 238
Axiom system for analysis and Skolem's theorem      242
Axiom system for set theory      240
Axiomatic method      3 17
Axiomatic set theory      18 235
Axioms of elementary number theory      155—157
Axioms of geometry      68
Bachmann, P.      14 27 315
Bar-Hillel, Y.      28
Basic equality sequent      290 300
Basic formula      74 75 81 116 216
Basic logical sequent      151 154 177 179 257 290
Basic mathematical sequent      151 177 257 260 290
Basic sequent      13 83 123 151 257 290
Behmann, H.      315 316
Benacerraf, P.      28
Bernays, P.      vi 1 2 6 8—10 20 24 26—28 201 313 315 317
Beth, E.W.      2 7 24—26 28
Black, M.      10 26
Bolzano, B.      3 24
Bound predicate variable      297
Bound variable      55 141 144 215 288
Brackets      54 71 141 215
Brouwer, L.E.J.      3 10 11 18 19 21 135 224 227 234 235 245—247 249 314—316
Calculability      245
Calculation procedure      158 159 161 175 239 244 245
Calculus      2 5 7 68 74 75 81 116 128 252
Calculus of natural deduction      2 7 68 81
Cantor, G.      3 10—12 16 26 230 242
Carnap, R.      315 316
Categorical algebra      2
Chain rule      180 seq.
Change of levels      281
Characteristic of an ordinal number      187
Characteristic significance of the characteristic for the reduction step      191
Choice      175—177 184 196—198
Choice set      217 222
Choice, set      217
Church, A.      24 27 239 240 245 315 316
Circulus vitiosus      134
CJ      293
CJ-inference figure      256 262 265 290
CJ-reduction      262 264

Classical analysis      18 246 247
Classical arithmetic      3 4 53 56
Classical logic      4—6 53 66 68 103
Classical predicate logic      4—6 66
Classification of forms of inference      144 148
Classification of mathematics      223
Classification of the forms of inference      144 148
Closed sentence system      38 39
Cluster associated with a formula      267
Cluster of formulae      267 269 302
Clustered formulae      266 302
Combinatorial topology      223
Combinatorial topology and the consistency proof      200
Comparison of different concepts of a derivation      181 260
Complete induction      12 68 145 153 154 180 183 190 194 197 205 207 231 256 309 314
Complete induction and completeness      154
Complete induction and consistency proofs      8 139 194 197 198 212 262
Complete induction and constructivism      225
Complete induction and the complexity of proofs      232 284 309 311
Complete induction and the correlation of ordinal numbers      188
Complete induction and the cut      262
Complete induction and the finitist interpretation      166
Complete induction in a derivation      309
Completed infinity      225 230 245
Completed infinity and mathematical existence      248
Completeness and complete induction      154
Completeness and Goedel's theorem      240
Completeness of axiom systems      238
Completeness of formalisms      7 143 198 233 307
Completeness of the rules of inference      154
Complex functions      224
Complex of elements      30
Complexity extremum      262
Complexity of a derivation      259 275
Complexity of a proof and complete induction      311
Complexity of a proof and the ordinal numbers      11 261
Conclusion of a "chain-rule" inference      181
Conclusion of a cut      31
Conclusion of a syllogism      32
Conclusion of an inference      30 148
Conditional truth      82
Conjunction      70 cf.
Connective      cf. also "Logical connective" "Logical
Connective, terminal      254
Consequence      2 3 33 cf.
Consistency      4 53 217 222 227 236 260 261
Consistency and constructive forms of inference      261
Consistency and derived concepts      157 193
Consistency and Goedel's theorem      197 229 232 233 236 238—240 284 287
Consistency and non-denumerability      247
Consistency and the axiom of infinity      222
Consistency and the empty endsequent      261
Consistency and the statability of a reduction rule      11 177 211 213
Consistency of analysis      12 15 16 136 227 232 236
Consistency of arithmetic      8 66 67 69 112 136 197
Consistency of arithmetic and Goedel's theorem      67
Consistency of classical arithmetic and Goedel's theorem      67
Consistency of classical predicate logic      103
Consistency of elementary number theory      4 8 132 136 228 240 287
Consistency of geometries      136
Consistency of intuitionist arithmetic      67
Consistency of intuitionist arithmetic and Goedel's theorem      67
Consistency of intuitionist predicate logic      103
Consistency of predicate logic      14 103 214
Consistency of propositional logic      214
Consistency of ramified analysis      14
Consistency of set theory      136 232 241
Consistency of the actualist interpretation      228
Consistency of the ramified theory of types      13
Consistency of the simple theory of types      13
Consistency proof      8 229 239 250
Consistency proof and algebra      200
Consistency proof and complete induction      8 139 194 197 198 212 262
Consistency proof and existential propositions      201
Consistency proof and Goedel's theorem      cf. "Goedel's theorem"
Consistency proof and Hilbert's programme      cf. "Hilbert's programme"
Consistency proof and indisputable forms of inference      138 171 193 228
Consistency proof and the natural calculus      252
Consistency proof and the statability of a reduction rule      11 177 211 213
Consistency proof and transfinite induction      8 231 232 261 286 297
Consistency proof for analysis      227 228 236 246 247 316
Consistency proof for elementary number theory      21 27 252
Consistency proofs and incompleteness      17 240
Constant symbol      70 111
Constant symbols      70 111
Construction rule      160 194 211 244
Constructive analysis and natural geometry      18
Constructive concept of a set      134
Constructive forms of inference in consistency proofs      261
Constructive, finitist, and intuitionist methods      18
Constructivism      cf. also "Idealism"
Constructivism and complete induction      225
Constructivist      227 239 250
Constructivist (intuitionist) analysis      18 244
Constructivist and indirect existence proofs      250
Constructivist concept of a number      244
Constructivist interpretation and Skolem's theorem      241
Constructivist interpretation of analysis      243
Constructivist interpretation of infinity      224 seq. 237 286
Constructivist objections to classical analysis      226 227
Constructivist point of view and indisputable forms of inference      228
Constructivist principle of set formation      225
Constructivist proof of the theorem of transfinite induction      285 286
Constructivist techniques and Goedel's theorem      239
Constructivist techniques in proof theory      228 237 239
Constructivist-concept of a set      134
Continuum      20 243 250 251
Contraction      84 256
Contraction in the antecedent      84 cf.
Contraction in the succedent      84 129
Contradiction      cf. also "Empty sequent"
Contradiction in mathematics      114 133 138 241 255
Contradictive derivation      261
Correctness of the rules of inference      159
Correlation of ordinal numbers with derivations      11 16 187 188 261 279
Correlation of values      305
Counterexamples      7
Craig, W.      7 25
Critical derivation      298 303
Critical reduction step      300 303 304
Curry, H.B.      6 18 21 24 25 28
Cut      2 5 15 31 32 84 256 312
Cut and complete induction      262
Cut and the Hauptsatz      5
Cut and the syllogism      32
Cut associated with a cluster      267 302
Cut element      31
Cut formula      256
D-formula      73
D-inference figure      73
D-S-formula      73
Davis, M.      24
Decidability of the predicate calculus and Fermat's last theorem      239
Decidable formula      269
Decidable formula in a proof      269
Decidable functions and predicates      160 174 194 199 211 288
Decidable predicate      160 174 194 199 211 288
Decidable proposition      159
Decidable propositions      160
Decision problem      6 66 69 238 239
Decision procedure      7 69 160 161
Decision procedure for predicate logic      239
Decision rule      161 198
Decision rule for predicates      160 198
Dedekind cut      224
Dedekind, R.      224 309
Deduction Theorem      311 cf.
Definability and the Herbrand — Gentzen theorem      7
Definite function      54 141
Definite number      141

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