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

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 $\mathfrak{A} (\left$b \atop c\right$)$       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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