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| Gentzen G. — The collected papers of Gerhard Gentzen |
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| 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  and  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  and  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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