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

Fixed Point Theorems of $\lambda$ -calculus      1101 (see also “Recursion Theorem and de Jongh’s Fix-point Theorem”)
Fixed Point Theorems, Brouwer’s      1002 1044
Floyd      580
Forcing (Cohen)      300 318 360 414f 641 699
Forcing (Finite Robinson)      90 159 160 170 171
Forcing (Infinite Robinson)      159 161 170 171
Forcing Base      98
Forcing conditions      415
Forcing in Infinitary Logic      98
Forcing Product of PO Sets      439f
Forgetful functor      115
Formally Intuitionistic Systems, Translation into      962
Formula      19 405
Formula, $\Delta_{0}$       238 409f
Formula, $\Pi$       239
Formula, $\Sigma$       239
Formula, atomic      18
Formula, Conjunctive Game      254
Formula, first-order      19
Formula, Minor      872
Formula, principal      872
Formula, side      872
Formula, Vaught      254
Fourman, M.P.      305 1053 1054 1060 1070 1081 1088
Fraenkel, A.A.      15 51 55 237 309 347 361
Fraenkel, A.A.,      363 364 365 370 404 454 547 637 784 815 840 1092
Fragment      250
Free algebra      287
Free variable      20
Frege, G.      6
Frenet, F. — J.      225
Freyd, P.      288 295 307
Fried      154
Friedberg Jump Theorem      638 639
Friedberg — Muchnik Theorem      645 661
Friedberg, R.M.      554 564 639 645 650 661 669 670
Friedman, H.      270 280 670 672 779 781 808 814 929 950 956 965 966 968 992 994
Frobenius, F.      295
Fubini, G.      375
Fuhrken, G.      68 100
Fukuyama      658
Functional      683
Functional, evaluation      685
Functional, Minimalization      686
Functional, Normal      697 714
Functional, Operative      687
Functional, Primitive Recursion      687
Functional, Signature of      683
Functional, Substitution      686 688
Fundamental theorem of calculus      214
Fundamental theorem of ultraproducts      112
G $\ddot{o}$ del Incompleteness Theorem      560 599
G $\ddot{o}$ del Numbering      547 633 647
G $\ddot{o}$ del, K.      6 10 16 23 35 41 51 55 57 195 199 234 343 350 359 378 400 404 427 441 451 454 455 463 465 466 489 534 547 556 560 564 597 599 642 647 650 654 657 704 784 750 751 752 754 755 756 757 758 805 807 814 825 826 851 865 868 869 917 920 921 939 957 958 961 962 963 964 969 970 975 980 982 986 987 988 1005 1027 1101 1106 1133 1136 1141
G $\ddot{o}$ del’s Functional (or Dialectica) Interpretation      963 1035
Gabbay, D.M.      620 621
Gabriel, P.      287 289 290 291 292 293 307
Gaifman, H.      141
Galaxy      204
Gale — Stewart Games      642
Gale, D.      642 643 807 808
Galvin, F.      389
Game Form Theorem      256
Games      748 769 “Determinacy” “Gale
Gandy — Kreisel — Tait Theorem      265
Gandy, R.O.      265 376 670 671 672 707
Gandy, R.O.,      735 736 740 768 771 772 773 776 777 780 781 934 952 953 956
Garavaglia, S.      101
Gauss, C.F.      198 205 206 217 218 220 221 225 226 227 228 229 289 346
GCH      see “Generalized Continuum Hypothesis)
Gel’fond, M.G.      1041
Generalization rule      32
Generalized Continuity      1019
Generalized Continuum Hypothesis      407 454 465
Generalized Continuum Hypothesis, Consistency of      426
Generalized Finite      655 657 658
Generalized Suslin Hypothesis      473
Generated Substructure      52 184
Generic Circle      292
Generic Extension      see Cohen Extension
Generic Model Theorem      91 99
Generic Sets      90 99 360 413
Generic Structure      288
Gentzen, G.      23 34 37 40 274 298 305 747 869 871 878 893 899 900 917 946 957 958 968 969 986
Gentzen’s Theorem      see “Cut-elimination Theorem”
Geometric morphism      300
Geometric Morphism/Functor      300
Gillman, L.      75 130
Girard, J. — Y.      969 1040
Giraud      299
Godel completeness theorem      32
Goldrei, D.C.      172
Good Ultrafilter      134
Goodman, N.D.      1017 1040
Gordan, C.      346
graphs      486
Gratzer, G.      120
Green, M.W.      533
Greenberg      153
Gregory, J.      270 476
Grilliot, T.J.      730 732 734 735 736 757 773 781
Grothendieck topos      298
Grothendieck, A.      296 298 299 303 311 1055 1088
groups      8 62 76 94f
Groups and Unsolvable Problems      578f
Groups, Abelian      8 611
Groups, Divisible      8
Groups, Existentially Closed      168f
Groups, free      54 97
Groups, Galois      72
Groups, Linear      121
Groups, matrix      62
Groups, Orderable      62
Groups, solvable      62
Groups, torsion      9 94 97
Groups, Torsion-free      9
Groups, Universal Locally Finite      190
Groups, Z      151
Grzegorczyk, A.      752 754 781 1100 1106
H( $\kappa$ ), $H_{U}(\kappa)$       244
Hahn — Banach theorem      354
Hahn, N.      354 355 357 929
Hajnal, A.      388 392 393 396 401 484 507 516 517 519 522
Haken, W.      579 580
Hakim      302
Hall, P.      284
Halmos, P.      372 404
Halpern, J.D.      366
Halting problem      538 569
Handbook, Cost of      see “Large Cardinals”
Hanf, W.      235 281 552 564 648 650
Hanf’s Theorem      648 650
Harnik, V.      256 266 267 269 271 275 278
Harrington, L.      643 662 671 672 675 734
Harrington, L.,      736 771 774 781 1133
Harrison, J.      277 952
Hatcher, W.      1086
Hausdorff, F.      27 60 75 84 102 128 136 352 353 356 357 519
Hechler. S.      508
Henkin Axioms      30
Henkin construction      31
Henkin, L.      23 28 30 31 32 33 36 39 57 58 78 102 297 671 757 860 864 865
Henrard, P.      142 160 161
Henrickson      75 130
Hensel, G.      149 150 151 644 649
Hensel’s Lemma      149 150
HEO      see “Hereditarily Effective Operations”
Herbrand Normal Form      889
Herbrand, J.      234 534 885 889 897 898
Herbrand’s theorem      876 898f

Hereditarily Continuous Functional      951
Hereditarily effective operations      1028
Hereditarily Finite Sets      43
Hereditarily Hyperarithmetic Operations      952
Hereditarily Recursive Operations      951 1027
Hermann, G.      126 127
Hermes, H.      346
Herstein, I.W.      117 124
Heyting, A.      974 977 982 995 1070
HFD Set      515
Hierarchy theorem      558f
Higgs, D.      299 311 1070
Higher Type Objects      see “Object of Higher Type”
Higher-order language      7 43 1060
Higman, G.      159 168 169 170 171 175 176 578 593
Hilbert — Bernays Completeness Theorem      860
Hilbert, D.      6 23 34 37 41 42 125 126 131 141 142 146 148 149 150 152 174
Hilbert, D.,      346 557 568 584 585 586 587 598 599 741 822 823 824 825 846 858 859 860 861 865 868 915 917 927 974 980 981 1004
Hilbert’s 17th Problem      148 149
Hilbert’s basis theorem      126
Hilbert’s Nullstellensatz      125 146
Hilbert’s program      598 822f 868
Hilbert’s Tenth Problem      568 584f
Hilbert’s Thesis      41 587
Hinata, S.      1036
Hindley, R.      1102
Hinman, P.G.      672 678 696 735 736 740 781
Hintikka Set      250
Hintikka, J.      249 251
Hirschelmann, A.      124
Hirschfeld, J.      142 167 168 172 207 231
Homeomorphy Problem      579f
Homogeneous Linear Ordering      65
Homogeneous model      75
Homogeneous-universal Structures      141
Homogenous Set      183 193
Homomorphic image      72
Homomorphism      72 108
Homomorphism of $\lambda$ -algebra      1100
Hopcroft, J.      584
Hopf algebra      288 308
Hopf, L.      288 308
Howard, W.      968 1011 1032 1034 1036 1037 1038
HRO      see “Hereditarily Recursive Operations
Hurd, A.      207
Hyland, J.      1125 1127 1128 1130
HYP(), HYP( $\mathfrak{M}$ )      245 246
Hyperarithmetical hierarchy      559 753
Hyperelementary      767
Hyperimmune      651
Hyperinteger      202
Hyperjump Hierarchy Comprehension Schemes      947
Hyperreal numbers      200 202
ICF      1028
Ideal      13 355
Ideal Statements      823
Ideal, maximal      14
Ideal, prime      14
Image (Homomorphic)      72
Immediate extension      150
IMP      826 836
Inaccessible cardinal      343 396
inclusion      310
Incompleteness Theorem, First      825 827 845 861
Incompleteness Theorem, Formalized First      852
Incompleteness Theorem, Formalized Second      828
Incompleteness Theorem, Second      825 828 846 862
Independent Theory      88
Index (of a Function)      538 702
Index (of the Handbook)      see “Self-reference”
Index Transfer Method      724 726 728
Indicator function      1141
Induction      739f
Induction Completeness Theorem      690
Induction on ordinals      331f
Induction on Sets      334
Induction on TC      243
Induction, Non-monotone      774f
Induction, on Unsecured Sequences      1009
Induction, Positive Elementary      764
Induction, Positive Existential      761f
Induction, transfinite      878 942 1011
Inductive definitions      526
Inductive Definitions, Dual of      749
Inductive Definitions, Theories of      968
Inductive Theory      55
Ineffable Cardinal      399 488
Infinitary Logic      43 97f 244f
Infinite Derivation      880
Infinite Derivation, Code for      886
Infinite hyperreal number      202
Infinite telescope      204
Infinite Terms      959
Infinite Terms, Normalization of      960
Infinitesimal Analysis      197f
Infinitesimal calculus      207 208f
Infinitesimal microscope      203
Infinitesimal number      12 198 202
Infinitesimal vector      215
Infinitesimally close      202
Infinity axiom      326
Instantaneous description      536
INTEGER      202
integral      213
Integral Definite Functions      152
Intermediate Value Theorem      1001 1042f
Internal Quantification      304
Internal Set      199 204 265
Interpolation theorem      72 272 “Suslin
Interpretation of $\lambda$ -terms      1098
Interpretation of a Language in a Topos      1076
Interpretation of One Theory in Another      598 612f
Interpretation of Terms of Forcing Language      413
Intuitionism      974
Inversion lemma      873 881 887
Isolated type      79 82
Isomorphic embedding      53
Isomorphism      53 109
Iteration of Forcing      see “Products of PO Sets and Martin’s Axiom”
Iteration theorem      see parameter Theorem
j      see “L and Oracle”
J $\acute{o}$ nsson, B.      69 73 74 75 76 82 83 84 88
J $\acute{o}$ nsson, B.,      141
Jacobson, N.      147 148 149
Jarden      154
Jech, T.J.      345 363 367 370 387 401 432 452 672
Jensen, R.B.      68 76 102 141 207 230 270 378 384 387 398 435 436 465 472 474 475 477 483 484 487 488 489 510 514 521 644 650 655 668 671 672
Jensenlehre      see “Fine Structure of L”
Jockusch, C.G.      641 643 644 648 649 650
Jockusch, C.G.,      672
Johnson, D.R.      207
Johnstone, R.      310
Joint embedding property      73 160 161
Jongh, D.H.J. de      979
Jonsbraten, H.      378 380 400 472 489
Jonsson Theory      73
Joyal, A.      174 294 295 296 300 301 305
Joyal, A.,      307 308 310
Juh $\acute{a}$ sz, I.      383 390 503 504 507 508 514 516 519
Jump Hierarchy Comprehension Schemes      947
Jump, Iterating      634 644 636
Jump, operator      551 558 634 638f 645 670
Jump, Theorems      638f
K $\ddot{o}$ nig, J.      126 136 383 384 394 395 927 928 953 1135
Kahr, A.S.      548 588
Kaiser Hull      157
Kaiser, K.      157
Kanamori, A.      398
Kaplansky      1 150 151
Karp, C.      97 98 99 102 235 236 281 465

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