Barwise J. (ed.) — Handbook of Mathematical Logic :: Электронная библиотека попечительского совета мехмата МГУ

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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

Collection Principles, $\mathbf{\Delta}_{0}$       239
Collection Principles, $\Sigma$       240
Coloring Infinite Maps      28
Combinatorial in L      474 479 483 “E-principle” “Kurepa “Square” “W-principle”)
Combinatorial Principles      423
Combinatory Algebra      1094
Comer, S.D.      174
Compactness Theorem      10 59 118 356
Compactness Theorem for propositional logic      26
Compactness Theorem, Proofs of      33 59 118
Companion of a Spector Class      778
Companion Operator      156f
Compatibility      412
Complete Formula      79
Complete r.e. set      543 553
Complete theory      16 50
Completeness      844
Completeness (of Intuitionistic Logic)      1025f
Completeness (of the Reals)      999
Completeness test      66
Completeness theorem      22f 844
Completeness Theorem for $L_{\omega_{1}\omega}$       99
Completeness Theorem for Categories      296
Completeness Theorem for L(Q)      44
Completeness Theorem, Barwise      236
Completeness Theorem, Extended      265
Completeness Theorem, Hilbert — Bernays      860
Completeness Theorem, Proofs of      36f
Completeness Theorem, Significance of      22f
Completeness Theorem, Statements of      35 39
Completeness, $\omega$       854
Completeness, Demonstrable      21 844
Completeness, semantic      854
Completeness, Syntactic      854
complexity      539 899f
Complexity class      539
Complexity of computation      539
Complexity of Decision Procedures      621f
Computability      see Effective Computability
Computation Record      536 540
Computational complexity      539 (see also “Complexity”)
Computers, digital      536
Concentrates      691
Conceptual Completeness Theorem      297
Condensation Lemma      465 (see also “Mostowski Collapsing Lemma”)
Condition for       89
Conjunctive Game Formula      254
Consequence      10 51
Conservation theorem      858
Conservative extension      56 932
Consistency Property      see “Hintikka Set”
Consistent theory      16 50
Constructibility      318 359 455 642f 649 654 667f
Constructibility, Axiom of      426 428 465
Constructivism      974
Constructivism, Naive      974
Constructivization, Global      1040
Constructivization, Local      1040
Context-free grammars      583f
Continuity Schema      1006
continuous      1000
Continuous Functionals, Extensional      1029
Continuous Functionals, Intensional      1028
Continuous, uniformly      1000
Continuum Hypothesis      318 344 376 407 420f 424f 454 465 635
Continuum Hypothesis and Martin’s Axiom      493 494
Contradiction, law of      25
Cook, S.A.      600 627
Cooper, S.B.      640 646 647
Corona problem      207
Coste      294 295 305 306 1054
Countable Functionals      1029
Countably compact space      508
Course-of-values      540
Coven, C.      153
CRA      974 990
Craig Interpolation Theorem      72 (see also “Interpolation Theorem”)
Craig, W.      72 102 235 272 273 274
Creative set      553
Critical Functions of Ordinals      945
Cross-section      151 152
CTM      see “Transitive Sets and Models”
Curry, H.B.      1092 1093 1095 1101 1105
Cut Rank      873
Cut rule      39 872
Cut-elimination theorem      40 875 882 888 898f
Cut-elimination Theorem for Infinitely Long Formulas      957
D1, D2, D3      see “Derivability Conditions”
Dalen, D. van      1025
Davis      41 528 564 567 585 586 589 590 592 593 594 650 807 808 813 814
de Jongh’s Fix-point Theorem      856f
de Morgan’s laws      25
Decidability in Topology      618
Decidable model      16
Decidable relation      535 (see also “Recursive Relation”)
Decidable theory      16 52 596f
Ded( $\kappa$ )      87
Dedekind Set      362
Dedekind, J.      84 87 362 365 366 378 379 380 385 386 925 926 954
Definability Lemma      416
Definition (in a Structure)      555
Degree Hierarchies      669
Degrees of Theories      647f
Degrees of unsolvability      550f 631f
Degrees, Automorphisms of      638 641 646
Degrees, Homomorphisms of      636f 641
Degrees, Isomorphisms of      638 641 645
Degrees, kinds of, $\alpha$ -degrees      633 660
Degrees, kinds of, Constructibility      642
Degrees, kinds of, Cuppable      638f
Degrees, kinds of, Exact Pairs of      637f
Degrees, kinds of, High      646
Degrees, kinds of, Kleene      728
Degrees, kinds of, Low      646
Degrees, kinds of, Minimal      636 638 640 647
Degrees, kinds of, Minimal a      661
Degrees, kinds of, R.E.      551f 634 640 645f 648f 650
Degrees, kinds of, Splitting      638
Degrees, kinds of, Turing      see “Degrees of Unsolvability”
Degrees, Sets of Determined Sets of      642f
Degrees, Sets of First-order Definable Sets of      640f
Degrees, Sets of Ideals of      636f 643 644 647
Degrees, Sets of Independent Sets of      635f
Degrees, Sets of Initial Segments      see “Ideals of Degrees”
Degrees, Sets of Semilattices      634f 645f
Degrees, Theory of      639 640f 646 647
Deligne, P.      296
Delta System      389
Demazure      293 307
Dense sets      412
Density theorem      645 661
Dependent Choice, Axiom of      358
Derivability conditions      827 839f
Derivation in Gentzen System      37
Derivative      208 212
Descartes, R.      289
Determinacy      642f 808
Determinacy, axiom of      369
Determinacy, Borel      643 651
Determinacy, Projective (PD)      642f 808
Devlin, K.      378 380 400 453 472 477 481 484 488 489 514 517 518 521 522
Diaconescu      310
Diagonalization lemma      827
Diagram      57
Dialectica interpretation      1032f
Diamond ( $\diamond$ )      318 378 510 517
Diamond ( $\diamond$ ), Consistency of      438
Differential      221
Differential closure      167
Diller, J.      1040

Dionne, J.      295 296 305
Diophantine Equations, Number of Solutions of      586f
Diophantine Relations      585f 588f
Direct limit      142 143
Direct Product of PO Sets      438
Directness      899f 904f
Discrete Orderings      603 604 610
Distributivity Conditions      see “Closure and Distributivity Conditions”
Doctrine      284 293
Dominating Families      496 497
Double negation, law of      25
Douwen, E. van      498
Dowker space      510
Dowker, C.H.      510 511
Downward Lowenheim — Skolem Theorem      64
Dragalin, A.G.      991
Drake, F.      397 400
Dries, L. van den      173 174 179
Driscoll, G.C.      660
Dyson, V.H.      1025
D’Alembert, J.      198 206
E-Principle of Jensen      474 517
E-Principle of Jensen, Consistency of      435f
E. — M.      see “Ehrenfeucht — Mostowski
Eastern Model Theory      48
Easton, W.      387 444
EC      see “Elementary Class
ECF      1028
EED      293
Effective computability      525 528 530
Effective procedure      528f
Effectively Enumerable Relation      541 (see also “Recursively Enumerable”)
Effectively Inseparable Sets      842
Ehrenfeucht — Mostowski (E. — M.) Set      184
Ehrenfeucht — Mostowski (E. — M.) Theorems      182
Ehrenfeucht, A.      98 182 184 186 187 189 193 612 628
Ehresmann, C.      292
Eklof, P.C.      97 105 127 136 141 155 158
Eklof, P.C.,      494 501
Elementarily equivalent      22 50 641
Elementary Analysis (Intuitionistic)      982
Elementary chain      55
Elementary Chain Theorem      56
Elementary class      22 50 112
Elementary diagram      58
Elementary embedding      53 143 186
Elementary extension      53
Elementary formula      253
Elementary in the Wider Sense      see “Axiomatizable and EC $_{\Delta}$ class”
Elementary map      see “Elementary Embedding”
Elementary Monomorphism      see “Elementary Embedding”
Elementary relation      253
Elementary substructure      53 185
Elementary topos      302
Elgot, C.C.      615 617
Elimination Mapping      1015
Elimination of quantifiers      55 146 147 155 600f
Elimination Theorem, First      1016
Elimination Theorem, Second      1016
Embedding theorem      363
Empty Theory      51
Encoding      see “Coding”
End-extension      247
Enderton, H.B.      527
Engeler, E.      81
Engelking, R.      1044
Ennis, G.      778
Entity      200
Enumeration Property      701 730
Enumeration theorem      704 715
Enumerative Systems      950
Envelope      728
Epstein, R.      647
Equality Axioms      29
Equalizer      1057
Equation calculus      656 899f
Equinumerous      336
Equivalent theories      50
Erd $\ddot{o}$ s — Rado Theorem      183 392
Erd $\ddot{o}$ s, P.      75 102 130 136 183 187 188 378 392 393 396 401 484
Ershov, Y.      17 132 136 141 148 149 150
Ershov, Y.,      153 620 628
Essential Unboundedness Theorem      850
Euclidean Geometry, Decidability of      596
Euler, L.      206 229
Excluded middle, law of      25
Existence and Minimality Lemma      414
Existence Theorem for Basically Saturated Models      75 76
Existence Theorem for Prime Models      80
Existence Theorem for Recursively Saturated Models      70
Existentially Closed Model      92 121 157f
Existentially Closed Number Theories      172
Existentially Closed Skew Fields      171 172
Existentially Complete      see Existentially Closed Complete
Existentially Universal (for a Theory)      162
Expansion of a Structure      30
Extension      305
Extension, Recursive      887
Extensional Structure      246
Extensionality axiom      325
Extensionality in Finite Types      931
Extensionality in Finite, Elimination of      934
External set      204
Fan Theorem      1012 1017
Feferman, S.      42 46 366 367 552 612 628 779 780 781 847 871 913 946 949 953
Feferman, S.,      961 962 965 968
Fenstad, J.E.      143 162 169 599 622 625 628
Field      15 69 72f 92f 119f
Field object      306
Field, $\mathcal{C}_{1}$       150 151
Field, algebraically closed      54 77f 92 93 146 147 608
Field, differential      84 87
Field, Differentially Closed      164f
Field, finite      153
Field, Laurent Series      150f
Field, non-Archimedean      12 199
Field, ordered      54 64f 74f 94
Field, p-adic      149f 611
Field, Pseudofinite      120 611
Field, real closed      130 147f 609
Field, separably closed      153
Field, skew      171 172
Field, Valued      133 149f
Filter      106
Filter, Cofinite      107
Filter, principal      107
Fine Structure of L      476 644
Finite character      61
Finite hyperreal number      202
Finite Hyperreal Vector      215
Finite intersection property      107
Finite Limits      1058
Finite products      1055
Finite Type Structures      919
Finite Type, Maximal      923
Finite Type, Minimal      924
Finite Types      1026
Finitely axiomatizable      22 50 119 647f
Finitely Generated Class of Functionals      703
Finitely Generated Model      52
Finitely satisfiable      58
Finitism      974 978
FIP      see “Finite Intersection Property
First Product Theorem      438f
First-Order Arithmetic (Intuitionistic)      982 (see also “Peano Arithmetic”)
Fisher, E.      143 162 169
Fitch, F.B.      34
Fitting, M.C.      980 981 1024
Fixed point      683 684
Fixed point theorems      856f

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