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Barwise J. (ed.) — Handbook of Mathematical Logic

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Название: Handbook of Mathematical Logic

Автор: Barwise J. (ed.)

Аннотация:

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 1165

Добавлена в каталог: 29.11.2009

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Предметный указатель

Poincar $\acute{e}$ , J.H.      915
Point      708
Point Projection      710
Point, Arity of      716
Point, Character of      718
Point, Type of      707
Point-Generator      1003
Pointclass      785
Pointclass, Properties of      730
Pointset of Type       728
Polish space      785
Polynomial time      627
Positive formula      72
Posp $\acute{i}$ $\hat{s}$ il, B.      382 385 509
Post Canonical Systems      755
Post Correspondence Problem      580
Post Words      572f
Post, E.L., Post      530 535 551 553 554 558 565 572 573 574 576 577 580 581 583 584 633 645 646 650 651 670 678 735 740 754 781
Post’s Problem      554 645f 661
Post’s theorem      558
Pour — El, M.B.      648
Power set      328
Power set, axiom      326
PR Formula      843
Praag, P. van      171
Prawitz, D.      968 980 981
Pre- $\lambda$ -Algebra      1098
Predicate calculus, intuitionistic      980
Predicates on Admissible Sets ( $\Sigma, \Delta, \mathbf{\Sigma}, \mathbf{\Delta}$ )      240
Predicativity      949 968
Presburger      67 151 599 603 606 617 625 628
Presburger’s Arithmetic      603 606 617 625
Preservation of Cardinals      422f 425f 443f
Pressing-down Lemma      374
Pretopos      297
Prewellordering      700 796
Prime formulas      23
Prime ideal theorem      356
Prime model      80 145 165 166 167 170 610
Primitive formula      843
Primitive function      831
Primitive Recursion, $< \varepsilon_{0}$ -Recursive      884
Primitive Recursion, Functional      681 884
Primitive Recursion, Test      145
Primitive recursive      534
Priority Method      554 640 645f 648 661
Productive function      553
Products of PO Sets      438f
PROGRAM      528
Progression rule      879
Projection      686 789
Projective determinacy      see “Determinacy”
Projective plane      306
Projective set      790
Projectum      478 666 668
proof      32
Proof-search Procedure      898f 904f
Proofhood, Decidability of      546f
Property      700 730
Property Theorem      700
Proposition al Logic      23
Pseudo-elementary Class      116
Pullback      1057
Putnam, H.      590 642 644 649 668 671 772
Putnam, H.,      975
Quantification Operators      935 936
Quantifier      44 694 769 770
Quantifier axioms      30
Quantifier, bounded      200
Quantifier, Dual of a      695 770
Quantifier, existential      695
Quantifier, Game      769
Quantifier, Monotone      770
Quantifier, Suslin      695
Quantifier, universal      695
Quasi-disjoint      see “Delta System”
Quine, W.      1059
r.e.      see “Recursively Enumerable”
RA      see “Recursive Analysis”
Rabin, M.O.      123 168 172 539 565 579 594 595 598 599 612 614 616 617 619
Rabin, M.O.,      620 624 625 628
Rado Selection Lemma      357
Rado, R.      183 187 188 357 392 393 396 533 565
Ramified analysis      948
Ramified Analytic Sets      948
Ramified Progressions of Theories      949 968
Ramsey theorem      183 392
Ramsey Theorem, Extension of the Finite      393
Ramsey theorem, finite      392
Ramsey, F.      183 187 390 391 392 399 400 500 643 917 928 953 970 1134 1135
Rasiowa, H.      1024
Real Number Generator      993
Real Numbers, Non-axiomatizability of      11
Real Statements      823
Realizability      987f 1018
Realize a Type      77 266
Realized Type      77
Recursion ( $\Sigma$ )      243
Recursion in Set Theory      333
Recursion on Ordinals      see “ $\alpha$ -Recursion”
Recursion operators      933 936
Recursion theorem      545 690 705 716
Recursive Analogues of Transfinite Number Classes      772
Recursive Analysis, Classical      975 991
Recursive Analysis, Constructive      974 990
Recursive function      529 531 560f 632 649 740 754
Recursive Function, General      534
Recursive function, primitive      534
Recursive Functional      540f
Recursive Functional of Finite Type      709 952
Recursive language      50
Recursive Operator      563f
Recursive ordinals      559 561f
Recursive real numbers      562f
Recursive relation      305 532
Recursive set      532 800 842
Recursively Axiomatizable Theory      50 547f 552
Recursively enumerable      542f 552f 570 800 841
Recursively Saturated Model      69
Redex      1102
Reduced product      109
Reducibility, many-one      544
Reducibility, One-One      544
Reducibility, Turing      550 (see also “Relative Recursiveness and Degrees”)
Reduct of a Structure      30 115
Reduction      276 795
Reflection Principle ( $\Sigma$ )      240
Reflection Principle (Proof Theoretic)      892
Reflection Principle (Proof Theoretic, Local      845f
Reflection Principle (Proof Theoretic, Uniform      845f
Reflexive Theory      851
Reflexiveness Theorem      851
Regular cardinal      372
Regular category      295
Regular set      665
Regularity axiom      326
Reid, C.      822 823
Reinhardt, W.      398
Relative Admissibility      242
Relative consistency      404
Relative Consistency Theorem      859
Relative Recursiveness      540 549f 633f
Relatively algebraically closed      144
Relativization      638 639 648f “Recursively “Roger’s “Reducibility”)
Relativization of Notions to Universes      924
Remarkable E.-M. Set      194
Replacement ( $\Sigma$ , $\Sigma_{1}$ )      241 658
Representability      751 753f
Representing Function      831
Resolvable Admissible Set      270

Ressayre, J.P.      82 237 266 267 269 271
Ressayre, J.P.,      276 281
Restricted Induction      931 967
Restriction of a functional      691
Reyes, G.E.      159 281 283 295 296 297
Reyes, G.E.,      301 302 305 310 313 1065
RFN      see “Reflection Principle (Proof Theoretic)”
RFN'( $\mathbf{T}$ )      845
Rfn( $\mathbf{T}$ )      845
Rham      208
Rice, H.G.      545 562 563 565
Rice’s theorem      545f
Richter, W.      740 772 773 780 781 782
Riemann, G.      198 206 213 214 580 927
Rings of Polynomials      54 97
Rings, Division      110 124
Rings, Local      296
Rings, Prime      123
Rings, Primitive      117 124
Rings, Principal Ideal      14
Rings, Regular      172f
Rings, Regular       173f
Ritt, J.      164
Robertson, E.      624
Robinson Consistency Theorem      71 (see also “Interpolation Theorem”)
Robinson, A.      12 48 49 54 58 62 71 72 89 94 99 100 103 123 124 125 126 130 131 137 140 141 142 144 145 146 147
Robinson, A.,      149 151 152 153 154 155 156 158 159 160 161 165 172 174 197 198 199 203 205 206 207 215 222 231 300 301 313 585 586 587 589 590 609 610 629
Robinson, R.W.      639 646 647
Robinson’s Test      144f
Robitaille — Gigu $\grave{e}$ re      305
Rogers, H.      528 529 537 565 638 640 649 651 660 674 677 692 737 781 917 940
Roger’s Conjecture      638
Rolle      607 1046
Rolle’s Theorem      1046
Rosen licht      167
Rosser, J.B.      534 840 841 842 855 1092 1096 1102 1120 1126
Rosser’s Theorem      841
Rosser’s Theorem, Formalized      854
Rotman, J.J.      578
Rowbottom      82 193
Rowland — Hughes, D.      143
Rudin, M.E.      136 307 491 510 514 522
rule set      741
Rule set, deterministic      744
Rule Set, Finitary      742
Rule Set, Recursive (r.e.)      751
Rule Set, Regular Arithmetical      752
Rule Set, Regular Elementary      757
Rules for $L_{\omega_{1}\omega}$       99
Rules for First-Order Logic Hilbert-style      31
Rules for First-Order Logic Hilbert-style, Gentzen-style      37 872
Russel, B.      6 322 339 351 363 917
Ryll — Nardzewski, C.      81 163 752 754 781
Sabbagh, G.      117 122 137 141 154 158 171 175 178
Sacerdote, G.      154 176
Sacks, G.      49 85 103 141 148 164 270 528 554 565 632 635 637 640 641 642 645 646 647 651 654 655 656 658 661 663 665 668 669 670 673 674 675 677 678 735 737
Sageev, G.      367
Samuel, P.      127 137
Samuel, P., $\hat{S}$ anin, N.A.      974 979 991
Samuel, P., $\hat{S}$ apirovskii, B.E.      507 509 522
Saracino. D.      141 142 159 163 164 172
Saracino. D.,      173 174
Sasso, L.      647
Satisfaction relation      20f
Satisfiable      50 69
Saturated model      76 128 134 147
Saturated Model, $\Sigma$       266
Saturated Model, Recursively      69
SCALE      810
Sch $\ddot{o}$ nfinkel      1092 1094 1095
Sch $\ddot{u}$ tte, K.      868 869 871 877 893 946 949 957 968 982
Schemata in Finite Type Theories      932
Schemata in Finite Type Theories, Choice      933 935 938
Schemata in Finite Type Theories, Comprehension      933 938
Schemata in Finite Type Theories, Second-Order      937
Schlipf, J.      266 968
Schoenfield, J.B.      46 148 155 324 398 400 412 414 415 416 452 495 501 528 559 560 565 578 594 632 639 640 645 646
Schoenfield, J.B.,      663 677 735 737 811 815 889 951 952
Schreier, O.      148
Schubert, H.      287
Schwichtenberg, H.      867 891
Scott, D.      38 103 149 235 276 282 299 310 327 400 452 649 651 677 861
Scott, D.,      1054 1055 1056 1060 1070 1081 1091 1100 1106 1107 1110 1128
Scott, W.R.      168 179
Second Product Theorem      440
Second-Order Arithmetic      168 639f
Second-Order Arithmetic (Intuitionistic)      983
Section      729
Section of Relative Primitive Recursive Functionals      961
Seidenberg, A.      126 127 137 164 165 166
Self-reference      1162
SemCompx      854
Semi-decidable Relation      541
Semi-recursive Relation      542f 693
Semi-recursive Set      542f 693 800
Semi-Thue Processes      571f 581f
Semigroups      576
Sentence, first-order      20
Separation axiom      325
Separation Schema      321f
Separation Schema, $\Delta$       241
Separation Schema, $\Delta_{0}$ -      239
Separation theorem      272 559 792
seq      834
Sequent      37
Sequentially compact space      509
Serret, J.A.      225
Set      811
Set and Martin’s Axiom      499
Set Mappings      485
Set Theory, Axioms for      15 321f
Set Theory, Consistency of      654
Set Tree      385 472 473
Sgro, J.      101
Sheaf      172f 298
Shelah, S.      82 87 89 103 135 137 140 143 160 161 164 167 190 196 486 494 495
Shore, R.A.      484 653 661 662 663 665 667 668 669 670 674 675 677 678
Sierpi $\acute{n}$ ski, W.      376 401 785 790 794 798 815
Signature of a Functional      683
Sikorski, R.      521 1024
Silver, J.      196 387 398 400 401 431 432 433 441 442 452 480 488 514 515 807
Simple model      122
Simple set      553
Simplified Form of a Point      716
Simpson, S.G.      631 639 640 641 643 644 650 651 661 662 669 670 671 672 675 677
Simultaneous Induction Lemma      687
Sinlmons, H.      142 143 155 161 163 170
Site      298
Skolem expansion      57 164 185
Skolem function      57 185
Skolem paradox      406
Skolem Relation      56
Skolem Term      185
Skolem, Th      6 10 12 23 33 44 45 48 49 56 57 63 64 65 66 67 68 71 81 95 97 100 130 140 163 185 186 187 188 190 193 194 195 236 245 247 255 256 262 374 406 152 466 467 469 477 478 480 487 608
Skolem, Th, y      612 618 620
Skolemization      164
Slomson, A^B.      106 119 122 131 134 135
Smorynski, C.      586 821 981 1024
Smullyan, k.M.      34 37 40 46 754 782
Soare, R.li      632 645 646 648 649 650 651
Sochor, A(      363 367
Solovay, R.      299 365 376 398 400 441 445 446 451 452 494 501 504 641 649 805 806 07 811 813 815
Solvable Term of $\lambda$ -Calculus      1117
Sound Theory      827 844
Soundness Lemma      35
Souslin Line      see Suslin Line
Space, Metric (Intuitionistic)      1002 1003
Specker, E.      276 636 637 639 652 768 771
Specker, E.,      774 782 953 954 968 1030 1038
Spector Class      767 777

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