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

Intuitionist logic      4—6 53 58 66 68 167 168
Intuitionist methods in proof theory      10
Intuitionist objections to consistency proofs      198 200
Intuitionist objections to consistency theory      200 201
Intuitionist predicate logic      4—6 66
Intuitionist propositional logic and the decision problem      6 69 103
Intuitionist propositional logic and the Hauptsatz      103
Intuitionist use of infinity      11
Intuitionist view of actualist propositions      19 21 229 247 249
Intuitionist view of the connectives $\supset$ and $\neg$       167
Intuitionist view of the elimination of double negation      168 169
Intuitionist view of the law of the excluded middle      3 169
Irrational number      243 244
IS      83
j      293
Jaskowski, S.      4 24
Johnstone, H.      25
Kalmar, L.      27
Kanger, S.      7 25
Kant, I.      19 22 28
Kemp Smith, N.      28
Ketonen, O.      7 8 25 26
Kleene, S.C.      7 9 25—27
Kneale, W.      5 25
Kneebone, G.T.      24
Kneser, H.      vii
Kolmogorov, A.N.      3
Kronecker, L.      224 244
L      293
L-system      4—7 25
Lambek, J.      2 24
Landau, E.      314
Langford, C.H.      25
Law of contradiction      79 86 154
Law of Double Negation      53 55 57 cf.
Law of the excluded middle      3 6 14 16 53 68 69 75 81 82 85 86 105 154 169 170 226 259
Leblanc, H.      5 25
Left rank of a derivation      89
Left side of a cluster      267
Legendre, A.M.      156
Level and degree      276
Level of a sequent      15 270 303
Levels of infinity      3 223
Levels of mathematics      3 223 233
Lewis, C.I.      6 25
LHJ      69 116
LHK      69 116 117
Lindemann, F.      316
Line of inference      255
Linear order of proofs      231
Linear sentence      30
Linear sentence system      2 39
LJ      69 81 82 86 105 106 115 116 123
LJ-derivation      83
LK      4 8 13 16 69 81 86 106 110 112 115 116 128 252 314
LK-derivation      83
Logic      3 68 314
Logical axioms      315
Logical connective      140 141 143 148
Logical consequence and derivability      2 3 24 33
Logical inferences and the antinomies      133
Logical symbol      54 70 313 cf.
Logicism      135 237
Logistic calculus      5 75 82
Lorenzen, P.      12 13 19 25 27 28
Lowenheim, L.      7
Lower formula      72
Lower sentence      31 32
Lower sequent      72 255
Lukasiewicz, J.      4
M      293
MacCall, S.      24
Major premiss      184
Mantissa of an ordinal number      187
Mathematical axiom      151 287 290 cf.
Mathematics over large finite domains      160
Matsumoto, K.      7 25
Maximal complexity      262
Maximal net      41 312
Measure of complexity      11 12 186 270 311
Meta logic      238 seq.
Meta mathematics      5 11 15 18 21 27 137 238 cf.
Meta theorem      cf. "Theorem in proof theory"
method      cf. also "Axiomatic method"
Method of infinite descent      15
Methods of proof      238
Midsequent      6 106 108
Minimal formula      142 159
Minimal term      142
MIX      88
Mix formula      88 207
Mix sequent      207
Modal logic      5—7
Model      7 136 224 241 243
Model for set theory      241
Modified concept of a derivation      179 287
Mostowski, A.      28
n-system      4 5
Natural calculus and consistency proofs      252
Natural deduction      2 4 7 25 74 75
Natural geometry      18 248
Natural geometry and constructive analysis      18
Natural geometry and physics      248
Natural intuitionist derivations      75
Natural numbers      53 136 142 223 230
Natural numbers and Skolem's theorem      243
Natural numbers and the antinomies of set theory      133 136
Natural numbers as ordinal numbers      232 284
Natural proof      263
Natural succession of inferences      293
Natural sum of ordinal numbers      278
Necessary and sufficient conditions for provability      8
Need for a constructivist consistency proof for classical analysis      246
Negation      66 67 70 155 cf.
Nest of intervals      245
Net element      41
Net sentence      41
NEW      287 seq.
NJ      68 69 75 82 115 116
NJ-derivation      75
NK      4 68 69 81 82 116 128 314
NK-derivation      81
Nonconstructive mathematics      18
Nondenumerability      229
Nondenumerability and consistency proofs      241
Nonderivability of the empty sequent      16 103
Nonderivability of the law of the excluded middle in LJ      105
Nonequality and negation      67
Nonexistence of a largest prime number      144
Nonstandard model      243 cf.
Normal form      312
Normal form of a proof      5 35 69 312
Normal form of complete induction      145
Normal Form Theorem      cf. "Hauptsatz" "Sharpened
Number theory      cf. "Arithmetic" "Elementary
Numeral      54 141 200 253
Numerical term      253 262 288 291
Numerical value      181
Numerical variable      288
Object      69
Object variable      70 111 140 314
Objects of analysis      223 224
Objects of finite mathematics      158
Objects of proof theory      138 194 211 228
Ohnishi, M.      7 25
Omission      cf. also "Contraction in the antecedent"
Omission of an antecedent formula      151
Omission of antecendent formulae      151
Operational inference figure      82
Operational inference figure schema      84 256

Operational inference figure schemata      84 256
Operational reduction      262—264 266 268 303
Operational rules      5 55 57
Operational rules of inference      5 55 57
Option      cf. "Choice"
Order of a derivation      107 108
Order of a sequent      15 cf.
Order type      285
Ordinal number      3 27 107 187 230 261 287 288 298 315
Ordinal number as measure of complexity      186
Ordinal number of a derivation      11 187—189 279
Ordinal number of the endsequent      279
Ordinal numbers and TJ-derivations      298
Ordinal numbers as measures of complexity      186
Partialaussage      164
Path      73 258
Peano axioms      136 314
Peano, G.      53 136 314
Philosophy and Hilbert's programme      21 237
Philosophy and the mathematician      234
Physics      21 227 249 250
Physics and classical analysis      18 247
Physics and natural geometry      248
Poincare, H.      3 224 316
Potential infinity      160 162 195 196
Prawitz, D.      5 24 25
Predecessor      27 110 111
Predicate      69 156 158 194 198 211 287 288
Predicate in elementary number theory      143 156
Predicate inference figure      107
Predicate logic      53 66 68 216 309 314
Predicate symbol      111 140 141 253 288
Predicate variable      289 292
Predicates in elementary number theory      143 156
Predicates in finite mathematics      158
Premiss      30 181
Prime      140
Prime formula      253 289 304 cf.
Prime number      144
Principal formula      87 256 304
Principia Mathematica      cf. "Russell-White-head"
Principle of duality      137
Procedure      cf. "Calculation procedure" "Decision
Projective geometry      137 247
Projective geometry and ideal points      247 250
proof      31 35 69 136 138 144 216 228 309 312 cf.
Proof by contradiction      cf. "Reductio (ad absurdum)"
Proof figure      66 72
Proof of a sentence      30
Proof of consistency      cf. "Consistency proof"
Proof of finiteness      191 seq. 195 197
Proof of finiteness and the indisputable forms of inference      193 195 197
Proof of the Hauptsatz      88 seq. 101
Proof of the Hauptsatz for LJ      101 seq.
Proof of the Hauptsatz for LK      88 seq. 106
Proof of transfinite induction      195 232 285—287 cf.
Proof theory      137 138 144 200 211 222 227 228
Proof theory, constructivist techniques in proof theory      228 237 239
Proof theory, fundamental principle of proof theory      162
Proof theory, intuitionist methods in proof theory      10
Proof theory, objects of proof theory      194 211 228
Properties of the derivation of the midsequent      114
Property of a critical derivation      304
Proposition      69
Propositional inference figure      107
Propositional logic      30 33 216 314
Propositional variable      54 70
Propositions and formulae      140 141
Provability      32 33 53 65 312
Provability and Fermat's last theorem      166
Provability and Goedel's incompleteness theorem      240
Provability and logical consequence      2 3 24 33
Pure (Euclidean) geometry      18 248 250
Purely logical formula      66 70
Purely logical proof      69
Purpose of the chain rule      181
Putnam, H.      28
Quantifier      4 54 70 77 cf. " " "
Quine, W.V.O.      20 28
Ramified analysis      12 14 15 cf.
Ramified theory of types      13 135 214 cf.
Rank of a derivation      89
Rasiowa, H.      7 25
Real function      243 245 246
Real number      14 136 224 241 243—246
Real numbers as ideal elements      250
Realism      19 cf.also
Recursive definition      27 53
Reduced form of a sequent      11 26 174 207
Reduced sequent      104
Reducibility of a derived sequent      285
Reducibility of a formula      262
Reducibility of an end sequent      317
Reducibility of an endsequent      317
Reducibility of the endsequent      317
Reducible formula      262
Reductio (ad absurdum)      79 153 168 169 181 204 206 cf.
Reduction of derived sequents      179 seq.
Reduction of true sequents      175
Reduction procedure      17
Reduction procedure and incompleteness      17
Reduction procedure and the indisputable forms of inference      197
Reduction rule      11 17 173 175 199 202—213
Reduction rule for basic sequents      177
Reduction rule for sequents over infinite domains      176
Reduction step      173 seq. 179 181 189 261 263 264 272 274 297 299
Reduction step and complete induction      180 183
Reduction step on a contradictive derivation      264
Reduction step on a derivation      179 seq.
Reduction step on TJ-derivations      299
Reinterpretation of theorems and proofs      223
Relative extremum      263
Relativity of the concept of a set      241
Replacement in a schema      76
Replacement of a free variable      57 113
Replacement of bound variables      57 113 152
Replacement of free variables      57 113
Replacement of propositional variables      57
Replacement of variables      57 76 113 152
Restricted transfinite induction      8 10 12 15—18 26 27 287 cf.
Restricted transfinite induction and incompleteness      16 17
Restricted transfinite induction and reduction rules      17
Restriction on LJ-inference figures      6 83
Restrictions on variables      58 84 117 153 216 255
Right rank of a derivation      90
Right side of a cluster      267
Rosser, J.B.      18 19 28
Rule of inference      5 151—155 159 216
Rules for $\forall$ and $\exists$ in the simple theory of types      216
Rules of Inference      5 151—155 159 216
Rules of inference and the "chain rule"      180 seq.
Rules of replacement      57 290
Russell's antinomy      3 133 162 214
Russell, B.      3 4 12 13 24 68 69 75 133 135 162 214 313 316
Russell, B. and Whitehead, A.N.      4 12 13 24 214 235
S      293
S-formula      72
Satisfaction      33
Schema for basic formulae of LHJ      116 117
Schema for CJ-inference figures      256
Schema for TJ-inference figures      291 298
Schmidt, H.A.      14 27
Scholz, H.      vi viii 24
Schroter, K.      2 24
Schutte, K.      12 14 15 27 28
Scope of a logical symbol      54
Second number class      10 16 26 230 233 286 307 308
Semantic tableaux      7
Semi-net sentence      42
Sense of actualist propositions      21 195 201 226 229 247 250

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