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Suppes P.(ed.) — Handbook of Proof Theory.Studies in logic the foundations of mathematics.Volume 137.
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Название: Handbook of Proof Theory.Studies in logic the foundations of mathematics.Volume 137.Автор: Suppes P.(ed.) Аннотация: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.
The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 821Добавлена в каталог: 05.03.2014Операции: Положить на полку |
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Предметный указатель
Clause, unit 24 Cleaveland, W.R. 776 Clegg, M. 604 631 Clique problem 615 Clocksin, W.F. 64 75 Closed 69 212 269 282 642 Closed recursive term 498 Closed under a rule 272 Closed under substitution 33 Closure ordinal 269 Clote, P. 96 144 145 206 403 542 543 546 571 605 625 630—633 781 Club 212 Co-product type 739 Cobham, A. 103 104 108 144 Cohen, L.J. 334 468 781 Cointerpretable 503 528 Collapsibly less, 244 Collapsing function 242 243 304 Collapsing Theorem 195 309 310 Collection 84 112 216 321 327 see Colon, M. 774 Combinator 69 344 360 423 429 715 Combinatory completeness 344 Commutativity 85 Compactness, propositional 8 Comparisons Lemma 160 Complement 19 Complementary relation 641 complete 4 Complete context 722 Complete induction 86 Complete justification 708 Complete partial order 748 Complete, implicationally 591 Completed definition 650 Completeness, combinatory 344 Completeness, cut-free 33 Completeness, first-order 30 Completeness, implicational 6 Completeness, infinitary 165 Completeness, interpretability logic 518 519 Completeness, modal logic 478—480 Completeness, paramodulation 63 Completeness, propositional 6 Completeness, provability logic see "Arithmetic completeness" Completeness, resolution 20 62 Completeness, SLDNF 671 Completion 650 Completion, Clark 650 Completion, partial 672 Composed set term 295 composition 96 103 Compound proposition 697 Comprehension 289 291 717 see "Arithmetical "Recursive Comprehension, axiom (CA) 271 366 379 446 Comprehension, axiom (CA), full 442 458 Comprehension, rule (CR) 279 Compton, K.J. 628 631 Computable real 762 Computation formula 183 185 186 Computational complexity, 245 Concatenation 124 425 Condensation Lemma 216 conditional function 103 Confluent 358 Consequence, 2-adequate 651 Consequence, 4-adequate 651 Consequence, lower 651 Consequence, upper 651 Conservative 506 Conservative Class 419 428 Consistent 30 138 506 530 see "Free-cut Consistent, 119 487 494 see Constable, R.L. 189 204 394 401 685 688 690—692 695 709 711 720—722 724 726 745 754 759 762 764—767 773 775—777 782 Constant objects functor 450 Constant symbol 26 Constructible hierarchy 215 267 Constructive ordinal 391 see Continuity, Generalized 427 Continuity, weak 434 continuous 212 Continuous cut elimination 265 Contraction rule 11 73 Contraction rule, 53 Contraction rule, propositional 53 Controlled access theories 722 Controlling operator 314 321 Cook, S.A. 74 101 108 144 340 364 365 401 434 461 463 550 552 592 594 595 616 624—626 629 631 633 686 Cook, W. 604 605 632 Coppo, M. 774 Coquand, C. 400 401 Coquand, T. 398 401 463 691 692 721 762 776 Cotolerance 503 528 530 Coullard, C.R. 604 605 632 Countable tree-ordinal 154 Counterwitness 504 Counting, length bounded 93 Course of values 223 Craig, W. 56—59 75 117 134 541 551 552 612 613 632 634 Crary, K. 768 776 Cremer, J.F. 776 Cresswell, M.J. 478 543 Critical function 383 Critical ordinal 214 Critical successor 516 Crole, R.L. 768 776 Crossley, J.N. 206 335 405 464 469 471 777 780 Cryptography 617 Cubarjan, A.A. 595 636 Curry — Howard isomorphism 47 68 500 751 752 see Curry, H.B. 47 68 76 500 546 727 751 774 776 Currying 343 Cut elimination 36 73 109 166 231 251 299 574 Cut Elimination Theorem 16 37 65 109 169 233 235 Cut elimination, continuous 265 Cut elimination, partial 657 Cut elimination, semantic 658 Cut formula 12 165 656 Cut free proof 12 Cut in a model 562 Cut in a model, inductive 98 118 140 562 Cut Rank see "Rank" Cut reduction lemma 168 Cut rule 11 231 554 656 708 Cutland, N.J. 164 204 Cutting plane proofs 604 616 D-interpretation 346 see D-interpreted 348 Dag-like proof see "Proof" Dahl, O.-J. 760 776 Damnjanovic, Z. 460 463 Database 23 63 Davis, M. 18 20 21 75 Dawson, J.W. 778 de Bakker, J. 784 de Bruijn, N.G. 688 690 721—723 727 755 774 de Jongh, D.H.J. 460 466 476 488 496 514 515 521 528 542 544 546 De Morgan, A. 164 220 de Rijke, M. 514 545 546 Deduction rule 600 Deduction Theorem 6 477 600 Definable function see also "Provably recursive" "Provably Definable function, 131 Definable function, 172 Definable function, 281 Definable function, 87 Definable function, 102 Definable function, relative 284 Definable predicate, 281 Definable predicate, 86 Definable predicate, 102 define 504 Definedness 411 715 728 745 749 Defining axiom 86—88 102 281 284 Definition by cases 423 Definition form 650 Dekker, J.C.E. 405 Demers, A.J. 757 776 Denotational semantics 759 Dependency graph 722 Dependent Choice (DC) 369 379 Dependent function 744 Dependent product 744 Dependent record 764 Dependent type 743 Depth, E-depth 53 Depth, formula 37 569 599 Depth, Kripke model 478 Depth, proof 569 599 Depth, term 567 Derivative 214 Derived model 480 Dershowitz, N. 358 401 descendent 12 32 Descendent recursive 266 see Descendent, direct 12 32 Descendent, immediate 12 Descent functional 159 Detachment Lemma 255 Di Prisco, C.A. 144 635 Diagonal Lemma 119 Diagonalizable algebra see "Magari algebra" Diagonalization 119 716 Diagram 219 Dialectica interpretation 338—340 346 458 see Dijkstra, E.W. 757 760 776 777 Dill, D.L. 775 Diller — Nahm interpretation 458 Diller, J. 339 340 352 401 434 458 459 464 Dimitracopoulos, C. 88 98 144 146 Directed 749 Directed acyclic graph 13 Discharge 47 Disjoint 613 617 Disjoint union 739 740 757 Disjunction property 66 Disjunction property, DP 419 432 Distinguished 222 Distributivity 85 divides 89 Division 89 Doets, K. 640 648 649 680 Domain 27 501 Domain closure axiom (DCA) 649 Domain theory 759 Domain type 715 Donahue, J. 757 776 Dorn, G.J.W. 773 Double-negative translation see "Negative translation" Dowd, M. 593 594 601 619 632 Downward persistency 301 Drabent, W. 672 680 Dragalin, A.G. 421 434 445 461 464 577 632 Dual 739 Duality 739 Dummett, M.A.E. 335 405 777 780 Dunn, J.M. 679 Dybjer, P. 692 777 Dzhaparidze, G.K. see "Japaridze G.K." Edalat, A. 759 777 Eder, E. 552 554 564 600 628 632 Edmonds, J. 604 631 Effective 453 Effective, canonically 453 Eggerz, P. 441 464 Egli, H. 759 777 Ehrenfeucht, A. 586 632 Eichenlaub, C.D. 690 775 776 Eigenvariable 32 48 110 Eklof, P.C. 9 75 Elementary Analysis (EL) 425 439 Elementary function 164 Elementary inductive definitions 270 Elementary topos 768 Elimination Lemma 236 258 Elimination rule 48 Elimination Theorem 237 Embedding theorem 179 Empty type 735 736 Endsequent 11 Enumerating function 212 Envelope 651 Epstein, G. 679 Equality axiom 29 32 63 233 341 648 656 Equality formula 642 Equality functional 430 Equality theorem 319 Equivalence class 720 Equivalence of readabilities 410 Esakia, L.L. 539 542 Essential reflexivity 493 Essentially 279 Essentially reflexive 505 Etchemendy, J. 690 773 Evaluates to (evals_to) 730 Exchange rule 11 Excluded middle, law of 64 342 Expansion, 51 Expansion, strong 51 Explicit Definability (ED) 432 Explicit Definability for Numbers (EDN) 419 Explicit definition 58 exponentiation 91 98 139 156 169 193 Exponentiation, ordinal 213 Exportation 301 Expression 295 Extended Axiom of Choice (EAC) 424 Extended Church's Rule (ECR) 419 439 440 Extended Church's Thesis (ECT) 416 438 Extended Frege see "Extension Frege system" Extended resolution 599 Extension 20 645 Extension Frege system 592 Extension variable 20 Extensional 121 Extensional Continuous Functionals (ECF) 433 Extensional equality 350 Extensionality 216 295 Extensionality, EXT 434 446 458 Extraction function, Ext 91 Factoring 61 Fairtlough, M.V.H. 80 153 164 190 204 242 Faithfully interpretable 485 503 528 Fan Functional 433 Fan Rule 434 436 Fan Theorem 366 428 Farmer, W.M. 554 571 632 691 777 Fast-growing hierarchy 152 158 195 Feasibly interpretable 514 Feferman provability 495 Feferman, S. 32 58 75 80 113 114 121 123 144 150 187 204 267 268 271 273 278 279 333 340 351 355 361 364 366 377 380 382—386 392 399 401—403 429 463 464 495 503 505 543 673 680 741 748 777 778 Fenstad, J.E. 402 404 405 472 635 680 Fermat's little theorem 720 Fermat, P. 720 Ferrante, J. 556 632 Ferreira, F. 377 402 460 464 Feys, R. 727 776 final 739 Finite subtheory 501 Finite type 343
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