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| Авторизация |
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| Gentzen G. — The collected papers of Gerhard Gentzen |
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| Предметный указатель |
Sense of directly proved propositions 165
Sense of ideal propositions 247 248
Sense of indirectly proved existential propositions 201 226
Sense of the results established in consistency proofs 200
Sense of transfinite propositions 161 162
Sentence 2 29 30 33 312
Sentence as a proposition 30
Sentence element 29 30
Sentence system 1 2 29 38 39 40
Sequent 2 71 82 150 151 252 254 255 289 314
Sequent calculus 5
Sequents and formulae 72
Set 133 215 216
Set of all sets 224 225
Set theory 137 cf. "Axiomatic
Set theory and Skolem's theorem 241
Sharpened Hauptsatz 6—8 15 25 106 110 112 313 cf.
Sharpened Hauptsatz and modal logic 6
Side formula 87
Significance of denumerability for consistency proofs 247
Significance of the constructivist point of view 250
Sikorski, R. 7 25
Simple theory of types 13 14 214
Simplification of a derivation 11 186 191 262 263 274 275 284
Simplification of a proof 11 186 191 262 263 274 275 284
Skolem's theorem 15 241—243
Skolem's theorem and constructivism 241
Skolem's theorem and denumerability 241 247
Skolem's theorem and elementary number theory 243
Skolem's theorem and Goedel's theorem 242
Skolem's theorem and the actualist interpretation 241
Skolem's theorem of relativity 241
Skolem, Th. xi 7 15 238 241—243 247 316
Statability of a reduction rule 173 175 196 204 206
Statability of a reduction rule and consistency 11 177 211 213
Statability of a reduction rule and the actualist interpretation 173
Statability of a reduction rule and the finitist interpretation 173 201 206
Statability of a reduction rule and the truth of a sequent 11 173 175—177 199 206 207
Strengthened Hauptsatz cf. "Sharpened Hauptsatz"
Structural inference figure 82 85 86
Structural inference figure schema 83 84 256
Structural inference figure schemata 83 84
Structural rules of inference 5
Structural transformation 151 180
Structural transformations and the "chain rule" 180
Structural transformations and the ‘chain rule' 180
Subcomplex and the assignment of truth-values 33
Subformula 71 159
Subformula property 6 87
Subformula property and the endsequent 6
Subst  214
Substitution of terms 299
Succedent 2 30 72
Succedent formula 151 254
Successor function 253
Syllogism 2 32 312 cf.
Symbol 53 54 69 70 140 141 313
Symbols as objects of proof theory 138 194 211 228
Symbols for definite functions 70
Symbols for definite predicates 70
Symbols for definite propositions 70
Symmetrization of sequents 259
Symmetry between the logical connectives 259
Symmetry of a formalism and the operation reduction 269
Symmetry of the schemata 86
Syntactic variable 54 70 90 142 152 214 255
Takeuti, G. 12—15 27 28
Tarski, A. 2 3 9 14 24 27
Tautologous sentence 30
Techniques of proof 139 143 237 242
Techniques of proof and incompleteness 308
Term 54 141 159 253 289 314 cf.
Terminal connective 254
Terminal number 297 299
Terminal symbol 71
Terminal symbol (connective) of a formula 71 254
Terminal symbol of a formula 71
| Tertium non datur cf. "Law of the excluded middle"
The ... such that 157
The classical calculus NK 75 81
Theorem 69
Theorem in a formal system 69 70
Theorem in proof theory 137 238
Theorem of transfinite induction 192 193 195 253 285 315
Thinning 30 83 255 cf.
Thinning and the syllogism 32
Thinning in the antecedent 83
Thinning in the succedent 83
Thomason, R. 25
TJ-derivation 287 291—293
TJ-derivation and the ordinal numbers 298
TJ-inference figure 291
TJ-upper sequent 291
Transferability of the consistency proof 198 199
Transfinite assumptions 165
Transfinite formula 142
Transfinite induction 231 232 284 cf.
Transfinite induction and Brouwer's proof of the uniform continuity of functions 246
Transfinite induction and elementary number theory 292 397
Transfinite induction and Goedel's theorem 16 239
Transfinite induction and the consistency proof 8 231 232 261 286
Transfinite induction theorem cf. "Theorem of transfinite induction"
Transfinite ordinal number 11 26 187 229 230 261 277 288
Transfinite ordinal numbers 11 26 187 229 230 261
Transfinite proposition 21 161 162 195
Transfinite propositions 21 161 162 195
Transfinite propositions and decision rules 161
Transfinite propositions and the elimination of the double negation 169
Transformation of a proof (derivation) 60 117 217 293
Trivial sentence 30
True formula 55 56 74 114
True proposition 54 217
True sequent 174 175 254 269 290
Truth of a formula 11 56 82 114 158 159 254
Truth of a minimal formula 159
Truth of a proposition in finite mathematics 158
Truth of a sequent 159 176 293
Truth of a sequent and the statability of a reduction rule 11 173 175—177 199 206 207
truth-values 33 159 161 218
Turing, A.M. 245 316
Tymieniecka, A. 24
TYPE 13 215 315
Universal quantifier 4 24 313 cf. "
Upper bound for the number of reduction steps 197
Upper formula 72
Upper sentence 31 32
Upper sequent 72 255 291
Uppermost formula of a cluster 262
Uppermost sequent 257
Urteilsabstrakt 165
Vaihinger, H. 19 20 28
Value of a derivation 298
Value of a term 159
Value of consistency proofs 200 201
Van der Waerden, B.L. 317
van Heijenoort, J. 24—28
Variable symbol 70
Variable term 253
Variables in elementary number theory 141
Variables of different type 215
Verscharfter Hauptsatz cf. "Sharpened Hauptsatz"
von Neumann, J. 236 313 314
Waisman, F. 20 28
Wang, H. 13 27
Weakness of the axiomatic method 240
Weierstrass, K. 17
Well-ordering of proofs 12 231
Weyl's concept of a number 244
Weyl, H. vii 3 21 24 165 224 234 235 244 245 249 314—317
Whitehead, A.N. 12 13 24 214 235
Woodger, J.H. 27
Zeller, Rev. 170
Zermelo — Fraenkel Axioms for Set Theory 240
Zermelo, E. 240 315
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