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Suppes P.(ed.) — Handbook of Proof Theory.Studies in logic the foundations of mathematics.Volume 137.
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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 821

Добавлена в каталог: 05.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$-Separation      280
$\epsilon$-calculus      31 554
$\epsilon$-number      157 202 213 392
$\epsilon_{0}$      157 213
$\exists$-free      413 416 440
$\Gamma_{0}$      214 383
$\lambda$-abstraction      68
$\lambda$-calculus      68 755 759
$\lambda$-term      68
$\Omega$ function      447
$\Omega$ functionset      451
$\Omega$ powerset      451
$\Omega$ predicate      447
$\Omega$ product      447
$\omega$ provability      487 494
$\Omega$ relation      447
$\Omega$ set      446
$\omega$-completeness theorem      224
$\omega$-consistent      see "Consistent"
$\Pi_{1}$-completeness      494
$\Pi_{1}^{1}$-Comprehension Theorem      287
$\Sigma$-Collection      280
$\Sigma$-Persistency      280
$\Sigma$-preservativity      488
$\Sigma$-Recursion Theorem      281
$\Sigma$-Reflection      280
$\Sigma$-Replacement      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 $(ATR_{0})$      268 399
Arithmetic translation      501
Arithmetic, bounded theories, $I\Delta_{0}$      84 98
Arithmetic, bounded theories, $S_{2}^{i}$, $T_{2}^{i}$      46 99 102
Arithmetic, classical second-order $(PA^{2})$      271 366
Arithmetic, Dialectica theories, $HA^{#}$, $PA^{#}$      352
Arithmetic, Dialectica theories, $\widehat{HA}^{#}$, $\widehat{PA}^{#}$      364
Arithmetic, extensional finite-type (E-HA)      430
Arithmetic, fragments of PA, $B\Sigma_{1}$, $B\Pi_{n}$      84
Arithmetic, fragments of PA, $I\Sigma_{1}$, $I\Pi_{n}$      46 84
Arithmetic, fragments of PA, $L\Sigma_{1}$, $L\Pi_{n}$      84
Arithmetic, Heyting's (HA, HA*)      341 409 412 488 721
Arithmetic, higher-order Heyting (HAH)      446
Arithmetic, inductive definition $(ID_{1})$      269 387 388
Arithmetic, intensional finite-type (I-HA)      430
Arithmetic, intuitionistic finite-type $(HA^{\omega})$      429 741
Arithmetic, intuitionistic first-order      see "Heyting's"
Arithmetic, intuitionistic second-order (HAS)      441
Arithmetic, iterated comprehension ($(\Pi^{1}_{1}-CA)$, $(Aut-\Pi_{1}^{1})$)      276 277
Arithmetic, iterated inductive definitions ($ID_{\alpha}$, $ID_{<\alpha}$)      270 273 274 392 399
Arithmetic, iterated inductive definitions ($ID_{\alpha}$, $ID_{<\alpha}$), autonomous (Aut-ID, Aut-BID))      274
Arithmetic, iterated inductive definitions ($ID_{\alpha}$, $ID_{<\alpha}$), with bar (BID)      273 274
Arithmetic, polynomial hierarchy, equational $(PV_{i})$      108
Arithmetic, polynomial time, equational (PV)      108 364
Arithmetic, polynomial time, finite-type ($PV^{\omega}$, $IPV^{\omega}$, $CPV^{\omega}$)      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 $\beta$      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, $I\Delta_{0}$      84 98
Bounded arithmetic, $S^{i}_{2}$, $T_{2}^{i}$      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 $\omega_{1}^{CK}$      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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