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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
Redex 358 Reduced sequence 222 Reduces 358 Reduces in one step 358 Reducibility candidate 397 Reducible 222 358 359 Reduction lemma 235 256 302 Refinement logic 704 Reflection principle 217 218 280 281 490 624 Reflection principle, iterated 495 Reflexive 505 Reflexivity 86 Reflexivity axiom 494 Regular axiom system 248 Regular counterwitness 504 Regular ordinal 211 Regular ordinals (Reg) 304 Regular ordinals (Reg), topological closure 304 Regular term 308 Regular witness 504 Reinhold, M.B. 759 782 Relation symbol 26 Relative translation 501 Relativization 118 216 Relativized 284 Relativizing formula 501 Remainder 89 Remmel, J.B. 206 471 630 631 634 781 Renardel de Lavalette, G.R. 425 429 441 470 546 replacement 84 94 109 110 112 135 412 445 447 see "Strong Reps, T. 708 784 Resolution 18—26 59—64 598—599 Resolution proof 20 Resolution refutation 19 598 Resolution rule 19 598 Resolution, ground 62 Resolution, hyper- 22 Resolution, input 24 Resolution, linear 24 Resolution, negative 23 Resolution, positive 22 Resolution, positive unit 25 Resolution, R-resolution 61 Resolution, semantic 23 Resolution, set of support 23 Resolution, SLD 26 640 661 Resolution, SLDNF 640 661 Resolution, unit 24 Resolvent 19 61 664 Restricted arithmetic (Arith) 711 Restricted quantifiers 215 Reverse mathematics 371 766 Rewrite System 358 Reyes, G.E. 721 782 Reynolds, J.C. 393 394 404 692 759 784 Rezus, A. 692 784 Richman's Principle (RP) 457 Richman, F. 457 463 469 767 782 Richter, M.M. 472 473 544 Ricks, K. 768 Riggle, M. 774 Riis, S. 629 636 Robbin, J. 189 206 Robinet, B. 404 784 Robinson arithmetic see "Q R" Robinson, A. 59 77 400 484 Robinson, e. 451 466 470 Robinson, G. 23 63 77 78 Robinson, J.A. 18 22 24 59 61 64 77 648 681 Robinson, R.M. 46 82 83 147 503 507 513 533 545 560 579 586 Robinson, T.T. 421 470 Rodriguez, R.V. 779 Rogers, H. 464 467—469 471 472 730 732 784 Root 478 Rose, G.F. 459 470 Rose, H.E. 189 206 404 Rosenfeld, J.L. 775 Rosolini, G. 451 466 470 Rosser ordering 496 Rosser provability 120 495 496 Rosser sentence 121 496 Rosser's Theorem 120 Rosser, J.B. 120 146 358 484 495 496 542—545 581 774 Roth, K.F. 628 634 Rudich, S. 134 146 Ruitenburg, W. 767 782 Run time typing 755 Rushby, J.M. 691 783 Russell, B. 31 77 600 634 636 685 687 694 698 714 727 728 758 784 785 Rydeheard, D.E. 783 Sambin, G. 401 476 484 541 542 545 Saracino, D. 400 Sasaki, J.T. 776 Satisfiable 4 19 28 Satisfied 28 Satisfy 28 61 Scarpellini, B. 470 Scedrov, a. 76 421 422 434 458 461 463 465 470 471 721 777 Schematic theory 115 117 552 554 Scheme 755 Schinzel, B. 544 Schlipf, J.S. 382 400 672 682 Schlueter, A. 267 304 335 Schmerl, U. 199 206 Schmidt, D. 154 206 463 Schmidt, H. 462 Schmitt, P. 780 Schroeder-Heister, P. 655 680 681 Schuette, K. 36 77 80 126 146 164 169 187 206 221 268 335 380 383 385 392 404 462 657 658 681 Schuetzenberger, M. 774 784 Schwichtenberg, H. 144 164 175 189 190 193 206 361 404 434 461 463 500 546 680 766 774 785 Scope 704 734 Scott, D.S. 204 428 445 448 464 471 509 545 723 757 759 777 784 Scott, p.j. 421 468 471 629 634 694 781 Scowcroft, P. 471 Search tree 221 222 228 Second incompleteness theorem 121 137 476 583 Second Incompleteness Theorem, formalized 506 Second order logic 271 Seely, R.A.G. 768 784 Seisenberger, M. 434 461 463 Seldin, J.P. 76 359 403 464 546 755 774 779 Self-realizing 415 Self-reference 118 Self-referential see "Diagonal Lemma" Selman, A.L. 775 Semantic resolution 23 Semantic tableau 36 Semantical Main Lemma 223 Semantics 27 Semi-formal calculus 231 234 298 Semiformula 31 Semiterm 31 Sentence 27 Sentential rule 317 Separated 453 Separated, canonically 453 Separation 216 321 Separation axiom 216 SEQUENCE 713 Sequence coding 91—94 Sequence-like proof see "Proof" Sequent 10 705 Sequent calculus 10 31 600 Sequent calculus, LJ 64 Sequent calculus, LK 32 Sequent calculus, PK 11 Sequent, empty 10 Sequent, initial 11 Sequent, upper, lower 11 Sequential theory 560 562 Set existence axioms 216 Set of support resolution 23 Set terms 295 Set theory 718 Set type 718 Setzer, A. 334 692 784 Sgall, J. 631 633 Shanin's algorithm 422 Shanin, N.A. 422 471 Shankar, N. 76 691 783 784 Shapiro, S. 468 Sharply bounded quantifier 82 Shavrukov, V.Y. 485 486 495 496 521 522 545 546 Sheard, M. 190 205 266 334 Shekhtman, V.B. 461 468 Shepherdson, J.C. 404 640 643 649 654 661 681 778 Shoenemann, R. 634 Shoenfield, J.R. 340 342 404 Shore, R.A. 471 766 782 Shostak, R.E. 690 711 784 Side formulas 12 Sieg, W. 111 143 146 178 190 204 206 333 339 372 382 386 401 402 405 463 Siekmann, J. 25 74 75 77 78 691 784 Signature 758 Simmons, H. 143 207 333 334 Simple contradiction 596 Simpson, S.G. 204 291 371 399 402 405 635 SIMULA 755 Simulate 624 Simultaneous inductive definition (SID) 676 Sipma, H.B. 774 Sitharam, M. 629 636 Size, proof 142 551 see proof" Size, term 567 Skeleton 42 114 568 Skolem function 50 Skolem functional 377 378 386 Skolem, T. 49—51 59 216 219 242 247 333 346 355 377 378 386 497 577 630 686 718 Skolemization 50 346 Skowron, A. 632 Skvortsov, D.P. 461 468 Skyrms, B. 144 204 Slagle, J.R. 23 77 Slash (|) 420—421 Slash (|), Aczel 421 SLD, SLDNF see "Resolution" "Completeness" "Soundness" Slisenko, A.O. 636 Slow-growing hierarchy 152 157 194 Slow-growing operator, G 152 156 Smash function (#) 81 99 100 Smith, B.C. 745 785 Smith, J.M. 401 461 471 691 724 782 Smith, S.F. 721 722 745 776 Smorynski, C. 114 122 147 476 477 484 487 492 494 495 504 545 Smullyan, R.M. 99 114 147 554 636 Social proof 2 Solovay function 482 Solovay, R.M. 98 118 126 140 145 147 154 191 205 476 481—483 485—489 492 495 496 514 522 532 534—536 539 540 543—546 557 562 589 590 636 778 Sommer, R. 126 143 147 175 190 199 204 206 Sorting 393 Sound 480 Soundness, 432 Soundness, first-order 30 33 Soundness, HA' 438 Soundness, HA* 414 Soundness, HA*, strong 414 417 420 Soundness, HA*, weak 414 417 Soundness, implicational 6 13 Soundness, intuitionistic many-sorted 448 449 Soundness, modal logic 478 Soundness, propositional 6 13 Soundness, resolution 19 Soundness, SLDNF 669 Space representable 161 Sparse set 626 Species 392 Specker, E. 144 Spector — Gandy Theorem 286 Spector( — Howard) interpretation 367 Spector, C. 286 340 349 350 366—371 393 395 396 400 405 Spectrum, 228 Spectrum, 247 Spectrum, 246 Speed up 497 Spivey, J.M. 766 785 Square root 90 Srivas, M. 783 Staal, J.F. 467 Staerk, R.F. 74 655 658 664 672 681 Stage in constructible hierarchy 215 295 Stage in constructible hierarchy, stg 295 Stage of an inductive definition 269 281 Standard interpretation 295 Staples, J. 429 458 459 471 Starting function 242 Static typing 755 Statman, R. 586 587 595 628 636 Stearns, R 686 779 Stein, M. 459 471 Stenlund, S. 724 745 755 785 Stern, J. 206 Stockmeyer, L.J. 100 106 147 Strahm, T. 268 334 335 423 471 Strannegard, C. 485 494 531 541 545 Stratification 728 Stratified program rules 660 Streicher, T. 461 471 Strict 411 447 Strong fragment 81 Strong inference 11 32 Strong interpretation 502 Strong replacement 96 109 110 Strongly critical 214 308 Strongly critical components, SC 305 Strongly critical, SC 214 Strongly normalizable 358 Strongly normalizing 358 Strongly positive 388 Structural rule 11 301 317 708 710 Structure 27 Structure, adequate 650 Structure, equational 648 Structure, four-valued 644 Structure, free term 670 Structure, Herbrand 645 Structure, lower three-valued 644 Structure, two-valued 644 Structure, upper three-valued 644 Structured tree-ordinal see "Tree-ordinal" Subformula 704 Subformula property 13 111 573 Subobject classifier 719 Substitution 5 27 59 116 341 567 648 728 734 Substitution Frege system 591 Substitution operator 232 Substitution rule 591 Substitution, closed under 33 Substitution, empty 648 Substitution, variable renaming 59 Subsume 22 Subsumption 22 Subtheory 501 Subtraction 89 349 Subtree ordering 154 193 Subtype 693 Succedent 10 Successor 96 103 220 232 344 360 409 423 429 516 Successor ordinal 211 304 Sudan, M. 630
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