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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Con_{T}$      828
$Con_{T}$, $1-Con_{T}$      852
$Con_{T}$, $k-Con_{T}$      853
$Con_{T}$, $\omega-Con_{T}$      853
$Con_{T}$, $\omega-Con_{T}^{G}$      853
$EC_{\Delta}$ Class      50 (see also “Axiomatizable”)
$k$-consistency      853
$l_{a}$      244
$L_{\infty,\omega}$-equivalent      97
$P = NP$ Problem      600 625
$Prov_{T}$      826 837f
$Pr_{T}$      826 838
$Pr_{T}^{R}$      841
$RFN'_{\Pi_{1}}$($\mathbf{T}$)      846
$RFN'_{\Pi_{n}}$($\mathbf{T}$)      849
$RFN'_{\Sigma_{n}}$($\mathbf{T}$)      849
$Rfn_{\Pi_{1}}$($\mathbf{T}$)      846
$Rfn_{\Pi_{n}}$($\mathbf{T}$)      849
$Rfn_{\Sigma_{n}}$ ($\mathbf{T}$)      849
$S$-Space      516
$S-m-n$ Theorem      544 705 715
$SynComp_{T}$      854
$Tr_{M}$      860f
$Tr_{n}$      844 850
$\alpha$ -Recursive      656-658
$\alpha$ -Recursively Enumerable      656—658
$\alpha$-Calculability      659
$\alpha$-Finite      657f (see also “A–finite)
$\alpha$-Recursion      653-679 885
$\alpha$-Recursive in      660
$\eta_{0}$-Set      128
$\eta_{1}$-Set      129
$\in$ -Model      64
$\L$os — Tarski Theorem      156
$\L$os — Vaught Test      66
$\L$os’ Theorem      see “Fundamental Theorem of Ultra-products”
$\lambda$      828
$\lambda$-algebra      1099
$\lambda$-Algebra, Extensional      1099
$\lambda$-Algebra, Hard      1100
$\lambda$-Algebra, Interior of a      1100
$\lambda$-Algebra, Sensible      1119
$\lambda$-Algebra, Weakly Extensional      1099
$\lambda$-calculus      1092f
$\lambda$-Definable Functions      1103
$\mathbb{E}$(T)      see “Category of Definable Types and Definable Total Functions”
$\mathbf{PRA}$      840 859
$\omega$ -Homogeneous Model      70
$\omega$ -Logic      42
$\omega$ -Pseudo Complete      133
$\omega$-Complete Theory      78
$\omega$-completeness theorem      78
$\omega$-consistency      825 85If
$\omega$-Consistency, Global      853
$\omega$-Consistency, Local      853
$\omega$-Consistency, Uniform      853
$\omega$-Parameterized Pointclass      730
$\omega$-Parametrization (of a Class of Functions)      702
$\omega$-rule      78 752 878
$\Omega$-set      1070
$\omega-Comp_{T}$      854
$\omega_{1}$-Incomplete Ultrafilter      129
$\omega_{1}$-Saturated      128
$\pi$-complete space      505
$\Pi^{1}_{1}$ Relations      752
$\pi_{1}, \pi_{2}$      830 834
$\Pi_{n}$ Formula      843
$\Sigma$-compactness theorem for Admissible Fragments      251 776
$\Sigma_{n}$ Formula      843
$\varphi_{f}$      838
*-finite (Star-finite)      213
*-Transform      199 200f
A-Finite      241 (see also “Generalized finite”)
A-Recursive      241
A-Recursively enumerable      241
Aanderaa, S.      578 588 592 740 772 780
Aarts, J.M.      505
Abel      206 928 955
Abramson, F.      1139
Absoluteness      408f 417
Abstract model theory      45
Acceptable structure      755
Acceptable structure, almost      768
Ackermann, W.      1139
Aczel, P.      696 697 735 736 739 740 768 771 772 773 776 780
Addison, J.W.      236 368 671 772 780 785 803 804 805 807 808 809 814 940
Adjan — Rabin theorem      579
Adjan, S.I.      579
Adler, A.      153
Admissible fragment      244
Admissible hull      246
Admissible ordinal      246 270 470 657f 772
Admissible set      239 470 655 774f
Algebraic theory      285
Algebraically closed model      121 (see also “Existentially closed”)
Algorithm      528 568
Almost disjoint sets      387f
Almost recursive      649 (see also “Hyperimmune”)
Alternating Chains, Method of      63
Amalgamation property      61 155
Amitsur, S.      124
Analysis      644
Analytic set      559
Analytical hierarchy      558f
Analytical Relations and Sets      555 802
Anti-Cohen PO Set      424
Antichain Conditions      422f 429f 441 444f
Antichains      413
Apartness      995
Applications to Algebra      see “the Particular kind of structure” e.g. “Field P-adic “Groups Torsion”
Applicative System      1094
Approximation of Game Formula      259 (see also “Stages of an Inductive Definition”)
Approximation of Terms in $\lambda$-calculus      1126
Approximation Theorem of $\lambda$-calculus      1127
Archimedian Axiom      12 202
Arithmetic Universe      307
Arithmetical Comprehension Scheme      937 938
Arithmetical hierarchy      556f
Arithmetical Relations and Sets      555f 802
Aronszajn tree      384
Aronszajn Tree and Martin’s Axiom      499
Aronszajn, N.      384 385 386 394 395 398 472 473 474 484 499 500
Artin, E.      131 132 141 146 148 149 151 152 609 1055 1088
Artin’s conjecture      132 147 150 151
Assignment to Variables      20
Atomic formula      18
atoms      361 (see also “Urelement)
Autonomous Progressions of Theories      949 968
Ax, J.      17 102 131 132 133 135 141 149
Ax, J.,      151 152 153 154 174 611 627
Axiom of Choice      335f 347 454 463
Axiom of Choice Dependent Choice      358
Axiom of Choice Intuitionistic Choice      986 987
Axiom of Choice Multiple Choice      365
Axiomatic Recursion Theory      669
Axiomatizable      22 50 112
Axioms and Rules for First-Order Logic      34 35 37 39
Axioms for $L_{\omega_{1}\omega}$      99
Axioms for a Theory      50
Axioms for L (Open)      101
Axioms for set theory      324
B$\acute{e}$nabou, J.      295 305 306
B$\ddot{o}$hm      1096 1101 1106 1119 1120 1121 1122 1123 1125 1126 1131
B$\ddot{u}$chi, J.R.      615 617
B$\ddot{u}$chi’s Theorem      615
Bachmann, H.      878 882 968
Back and Forth Construction      71
Bacsich, P.      122 135 143
Baire      159 365 369 377 379 380 492 497 501 504 505 506 785 798 813 928 1004
Baire property      504 798
Baire Property and Martin’s Axiom      492 497
Baire space      785
Baldwin, J.      88 164
Banach — Tarski paradox      351
Banach, S.      351 352 353 354 355 357 375 400 808 927 929
Bar induction      942 954. 1010
Bar Theorem      1010
Bar — Hillel, Y.      347 679
Bar-recursion      1031
Barendregt, H.      1091 1093 11
Barendregt, H., U      1 1105 1117 1125
Barr      298
Barwise compactness theorem      see $\Sigma$-Compactness Theorem for Admissible Fragments
Barwise Completeness Theorem      236
Barwise Completeness Theorem, Abstract Form      262
Barwise Interpolation Theorem      273
Barwise, J.      5 45 58 69 94 97 100 101 141 159 160 235 236 237 238 242 246 251 262 263 265 273 274 275 278 280 325
Barwise, J.,      397 400 655 670 671 777 778 780 955 968
Basic formula      74
Basic Omitting Types Theorem      93
Basic Stability Function      87
Basic Stone Space Over $\mathfrak{M}$      84
Basic type      74
Basic Type Over $\mathfrak{M}$      82
Basic-Stability Spectrum      87
Basically $\kappa$-Stable      86
Basically Saturated      74
Basis      803
Bastiani, A.      292 311
Baumgartner, J.      387 399 499
Beck      295
Beeson, M.J.      1022
Behrens, M.F.      207 209
Belegradek, O.B.      164 169 170
Bell, J.L.      106 119 122 131 134 135
Bendixson, I.      84 85 749 784 955
Berkeley, G.      205
Bernays, P.      51 55 860 861 865 868 917 939 974
Bernstein, F.      353 516
Bertrand, J.      367
Beth, E.      34 44 236 274 280 980 1024
Beth’s Theorem      274
BHK-explanation      977 982
Binary expansion      998
Binumerate      838
Bishop, E.      926 927 929 974 1045 1046
Blackwell, D.      808
Blass, A.      366
Blocking Requirements      615 (see also “Priority Method”)
Blum      539
Blum, L.      101 148 149 166
Boffa      171 175
Bohm Trees      1120
Bohm’s Theorem      1106
Boileau, A.      299 305 1054
Bold Face $\mathbf{\Sigma, \Pi, \Delta}$      240
Bolzano — Weierstrasz Theorem      1042
Bolzano, B.      198 1042 1043
Boolean algebras      54 89
Boolean Extension      174
Boolean power      163
Boolos — Putnam Theorem      644 649
Boolos, G.      642 644 649 668 671
Boone, W.W.      169 578 579 580 593
Borel hierarchy      788
Borel set      750 787
Borel, F.      358 377 498 750 753 785 787 915 917 925 928 929 955
Box ($\Box$) Principle of Jensen      see Square Principle of Jensen
Boyd, R.      644
Brady, A.H.      533
Bridge, J.      968 1091
Britton, J.L.      578
Brouwer, L.E.J.      822 823 825 915 927 942 974 977 982 1002 1005 1010 1042
Brouwer, L.E.J.,      1045
Bruce, K.      100
Buchholz, W.      968
Bunge      299 310
Burgess, J.P.      403 492
Burkhoff, G.      173
Busy Beaver Problem      533
C.U.B.      see “Closed Unbounded Set”
Cannonito, F.B.      578
Canonical structure      31
Cantor — Bendixson Construction      749
Cantor — Bendixson derivative      84
Cantor — Bendixson rank      85
Cantor — Bendixson Theorem is False in HYP      955
Cantor, G.      84 85 203 206 207 253 261 263 272 277 346 347 348 353 608 618
Cantor, G.,      784 925
Cardinal      336f
Cardinal, regular      372
Cardinal, singular      372 (see also “Large Cardinals”)
Cardinality of a Model      63
Cardinality Spectrum      88
Carson, A.B.      142 172 173
Cartesian Category/Theory      290 1056
Categorical theory      66 607
Categorical Theory, $\mathbf{\aleph_{0}}$      163
Categorical Theory, $\mathbf{\aleph_{1}}$      164
Category of Definable Types and Definable Total Functions      1065
Category of models      114
Category of T-algebras (Models)      285
Cauchy, A.      133 198 206 208 211 212 214 215 219 563 925 926 928
Cauchy, A., $\hat{C}$ech, E.      357 382 385 501 507 509
Cauchy’s Principle      211
CCC (Countable Antichain Condition), Partial Orders      492
CCC (Countable Antichain Condition), Spaces      390 492 493 505
Ce$\hat{i}$tin, G.S.      564 1008
Cenzer, D.      670 671 740 772 780
ch      see “Continuum Hypothesis”
Chain conditions      see “CCC” “Antichain
Chain of Models      55
Chang — $\L$os — Suszko Theorem      63 156
Chang, C.C.      45 49 63 68 76 102 106 132 134 136 142 143 144 156 157 163 196 277 280 487 488 757 780
CHARACTER      718
Characteristic function      302
Characteristic of a field      15
Characterization Theorem (for Realizability)      989
Characterization Theorem (for the Dialectica Interpretation)      1035
Cherlin, G.      159 172
Chevalley, C.      295
Choice function      335 347
Choice sequences      1005
Choice Sequences, Elimination of      1012f
Chong, C.T.      662
Chromatic number      486
Church — Kleene $\omega_{1}$      772 (see also “Recursive Ordinals”)
Church — Rosser Theorem      1102
Church, A.      51 235 533 534 535 541 564 568 571 585 592 599 753 771 772 800 865 917 986 1007 1092 1093 1095 1096 1100 1102 1106 1120 1126
Church’s Thesis, Extended      989
Circular Reasoning      see “Vicious Circle Principle”
Classes in Set Theory      338f
Classifying topos      301
Closed unbounded set      372f 407
Closure and Distributivity Conditions      424f 429 434f 443
Co-recursively Enumerable      647f
Coalgebras      288
Cobham, A.      51
Code      826 830f 835f
Code (of a Function)      702 (see also “Index”)
Coding of Tuples      536 693 702
Coding scheme      755
Cohen Extension      414
Cohen PO Set      420
Cohen, P.J.      89 147 148 151 152 154 159 300 359 360 363 365 368 404 406 412 414 420 421 423 424 427 451 606 628 641 784 814
Coherent theory      296
Cohn, P.M.      168 171 284 287
Cole, J.      308 310
Collapsing Cardinals      422 441
Collapsing PO Set of L$\acute{e}$vy      441
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