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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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280 31 554 157 202 213 392 157 213 413 416 440 214 383 68 68 755 759 68 447 451 451 447 447 487 494 447 446 224 see "Consistent" 494 287 280 280 488 281 280 280 Aagaard, M. 783 Abadi, M. 759 773 Abramsky, s. 74 759 773 Abstraction 423 Acceptable operator 301 Accessibility inductive definition 388 391 392 Accessibility relation 478 Accessible part 271 Ackermann — Peter function 242 Ackermann, W. 31 76 126 143 174 189 203 242 553 633 Active formula 42 Active sequent 34 Aczel, P.H.G. 143 207 333 334 385 392 399 421 457 462 718 729 730 745 767 773 Addison, J. 385 Additive components 213 Additive connective 71—73 733 Additive normal form 213 Additively indecomposable 212 308 Adequate 479 516 519 see "Structure" Admissibility predicate 283 Admissibility predicate, axioms (Ad1)-(Ad3) 283 Admissible 217 304 Admissible, believes to be 218 Agliano, P. 542 Aitken, W. 773 Ajtai, M. 604 605 607 617 618 621 629 Algol 755 Ali, M. 779 Allen, S.F. 691 692 709 720 723 745 747—749 766 768 773 776 Alon, N. 616 630 Alur, R. 774 783 Analysis 366 395 see Ancestor 12 32 Ancestor, direct 12 32 Ancestor, immediate 12 Anchored 43 46 110 112 Anger, F.D. 779 Antecedent 10 Anti-idempotency 86 Antisymmetry 86 Application 715 Apt, K.R. 640 648 649 661 679 Arai, T. 203 204 267 Arithmetic see also "Bounded arithmetic" "Number "Peano Arithmetic completeness 476 481 483 485 489 Arithmetic completeness, classification theorem 490 Arithmetic hierarchy 83—85 170 Arithmetic realization 476 491 496 499 521 532 Arithmetic transfinite recursion 268 399 Arithmetic translation 501 Arithmetic, bounded theories, 84 98 Arithmetic, bounded theories, 46 99 102 Arithmetic, classical second-order 271 366 Arithmetic, Dialectica theories, 352 Arithmetic, Dialectica theories, 364 Arithmetic, extensional finite-type (E-HA) 430 Arithmetic, fragments of PA, 84 Arithmetic, fragments of PA, 46 84 Arithmetic, fragments of PA, 84 Arithmetic, Heyting's (HA, HA*) 341 409 412 488 721 Arithmetic, higher-order Heyting (HAH) 446 Arithmetic, inductive definition 269 387 388 Arithmetic, intensional finite-type (I-HA) 430 Arithmetic, intuitionistic finite-type 429 741 Arithmetic, intuitionistic first-order see "Heyting's" Arithmetic, intuitionistic second-order (HAS) 441 Arithmetic, iterated comprehension ( 276 277 Arithmetic, iterated inductive definitions ( 270 273 274 392 399 Arithmetic, iterated inductive definitions ( 274 Arithmetic, iterated inductive definitions ( 273 274 Arithmetic, polynomial hierarchy, equational 108 Arithmetic, polynomial time, equational (PV) 108 364 Arithmetic, polynomial time, finite-type ( 364 365 Arithmetic, primitive recursive (PRA) 364 372 Arithmetic, primitive recursive analysis 264 Arithmetical 224 Arithmetical axiom 101 176 177 Arithmetical comprehension (ACA) 273 379 Arithmetically definable 269 Arithmetization of metamathematics 113—118 Arora, S. 550 630 Array 713 756 Arteemov, S.N. 485 487 489 490 497—499 532 534 535 540 541 assertion 694 698 ASSIGNMENT see "Truth assignment" Associativity 85 Atomic formula 26 642 703 Atomic set term 295 Attribute grammar 708 AUTOMATH 721 Automath book 721 Autonomous iteration 385 Autonomous ordinal 383 385 Autonomously inaccessible 267 Auxiliary formula 12 Avigad, J. 80 123 126 143 190 204 340 372 399 400 Avron, A. 485 541 Axiom 751 Axiom 286 288 Axiom of Choice 347 352 367 379 717 see Axiom of Choice, AC 271 432 Axiom of Choice, Extended 424 Axiom of Choice, quantifier-free 426 Axiom of Choice, Rule (ACR) 432 Axiom Schema 591 Axiomatible 117 Axiomatization 29 551 Baaz, M. 554 568 573 587 628 630 Bachmann hierarchy 385 Bachmann — Howard ordinal 193 196 268 385 391 392 Bachmann, H. 193 196 206 268 385 391 392 400 Backhouse, R.C. 691 773 bar 367 Bar Induction (BI) 272 273 366—368 428 Bar recursion 366 368 Bar rule 273 383 Bar Theorem 368 Bar-Hillel, Y. 144 467 Barbanera, F. 459 462 Barendregt, H.P. 429 462 755 773 Barwise, J. 57 58 74 75 77 143 147 205 206 217 229 267 269 280 281 283—285 291 333 382 400 401 404 405 462 469 472 545 635 682 690 773 BASIC axioms 101 Basic Set Theory, BST 280 Basin, D. 709 773 Bates, J.L. 754 766 773 Beame, P. 599 604 607 618 621 630 635 Beckmann, A. 210 227 254 333 Beeson, M.J. 340 357 366 401 411 421 429 436 441 458 462 463 721 774 Beklemishev, L.D. 486 487 489 490 492—496 528 541 Bell, J.L. 694 718 719 741 774 Bellantoni, S. 607 630 Bellin, G. 73 74 Belnap, N.D. 643 679 Bennett, C. 99 Bennett, J.H. 98 99 143 Berardi, S. 463 774 Berarducci, A. 488 519 521 522 530 542 Berger, u. 434 461 463 766 774 Bernardi, C. 484 542 Bernays, P. 31 76 117 145 339 476 481 506 543 554 555 560 586 633 718 774 Berry, G.G. 113 Beth's definability theorem 58 Beth, E.W. 36 58 59 74 484 545 554 630 Bezem, M. 436 463 465 Bibel, W. 780 Bimodal logic 491 494 539 Bimodal logic, type 492 Binary tree 371 Binding occurrence 734 Binding phrase 714 Binumerate 504 Bishop, E. 356 401 725 729 762 767 774 Bjorner, N. 691 774 Blair, H.A. 653 680 Blankertz, B. 253 300 333 Blass, A. 74 Bledsoe, W.W. 690 711 774 775 Block opener 721 body 649 Boehm, H.-J. 757 767 774 Boerger, E 472 473 544 633 635 Boffa, M. 462 464 Bogdan, R.J. 784 Bol, R. 640 661 679 Bonet, M.L. 600 605 616 617 630 Boolean circuit 595 Boolean circuit, bounded depth 607 Boolean circuit, monotone 615 Boolean function 3 Boolean proposition 702 Boolos, G. 113 122 143 475—477 485 487 488 490 494 495 532 533 542 Boone, W.W. 78 Bootstrapping 85 89 Boppana, R. 616 630 Borel, F. 371 Bound variable 27 69 704 734 Bounded arithmetic 97 139 364 Bounded arithmetic and propositional logic 619 Bounded arithmetic, 84 98 Bounded arithmetic, 99 102 Bounded consistency 138 Bounded formula 83 170 437 439 Bounded proof 138 Bounded quantifier 82 109 Bounded set 211 Bounded theory 82 97 Boundedness lemma 225 Boundedness Theorem 224 303 Bounding Lemma 170 172 Bounding term 88 Bourbaki, N. 714 717 718 738 758 774 Boyer, R.S. 690 711 774 775 Boyle, J. 77 786 Braffort, P. 782 Bridges, D. 729 767 774 Bromley, H.M. 776 Brouwer — Heyting — Kolmogorov (BHK) interpretation 65 408 Brouwer, L.E.J. 65 151 228 366—368 402 408 686 727 774 780 785 Brown, A. 774 Broy, M. 773 775 Buchholz, W. 153 164 189 190 199 201 203 204 242 249 253 254 266 300 332—334 385 392 401 402 418 463 662 680 Bundy, A. 689 775 780 Burch, J.R. 766 775 Burnside, W. 78 Burr, W. 386 401 Buss, S.R. 46 74 80 88 92 97 99 101—105 107 108 110 114 117 126 127 130—135 138 143 144 190 204 364 401 407 434 461 463 481 488 541 554 571 586 587 589 599 600 604 605 618 619 622—627 629—631 634 686 769 775 Butts, R.E. 472 Calculus of constructions 398 Calculus of problems, Medvedev's 461 Call by name 715 Call by value 715 Cancellation law 85 86 Cancellation of double negations 438 Cannonito, F.B. 78 Canonical proof 725 Canonical realizer 415 Canonical term 116 119 Canonical value 745 Canonically false proposition 697 Canonically true proposition 694 697 Cantini, A. 377 401 Cantor Normal Form 126 157 185 196 213 Cantor, G. 126 157 185 196 213 237 300 716 718 768 Cantorian closed 300 Carbone, A. 542 Carboni, a. 463 Cardelli, L. 759 773 775 Cardinal 211 Cardinal term 308 Cardinality 211 Carlson, T. 493—495 542 Carson, D.F. 23 78 Cartesian product 343 696 756 Cartwright, R. 774 Category theory 768 Cavedon, L. 668 680 Cedent 10 Cellucci, C. 463 Chaitin, G.J. 113 144 Chan, T. 690 711 775 Chang, C.-L. 24 25 64 74 552 567 628 631 Chang, C.C. 758 775 Chang, E. 774 Characteristic set 254 296 Characterization theorem 416 Chellas, B.F. 478 542 Chew, L.P. 685 767 775 Chirimar, J. 762 767 775 Choice see "Axiom of choice" "Dependent Chomsky, N. 727 775 Church — Rosser property 358 Church's thesis 415 Church's Thesis, Church — Kleene ordinal 217 222 see Church's Thesis, CT 433 437 Church's Thesis, Extended 416 438 Church's Thesis, Weak Extended 440 Church's Thesis, with Uniqueness 437 Church, A. 146 358 391 415 416 419 420 422 433 434 437 440 442 476 686 688 694 695 711 714 727 730 741 755 758 774 775 777 Cichon, E.A. 153 190—193 199 201 204 249 266 333 Circuit see "Boolean circuit" Clark's equational theory (CET) 648 Clark's equational theory (CET), standard model 648 Clark, K.L. 640 648 650 661 669 673 680 Clarke, E. 468 766 775 class 718 Class terms 280 Classification Theorem 202 490 Clause 19 598 Clause, ground 62 Clause, mixed 19 Clause, negative 19 Clause, positive 19 Clause, program 649
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