Steen S. — Mathematical Logic with Special Reference to the Natural Numbers :: Электронная библиотека попечительского совета мехмата МГУ

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Steen S. — Mathematical Logic with Special Reference to the Natural Numbers

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Название: Mathematical Logic with Special Reference to the Natural Numbers

Автор: Steen S.

Аннотация:

This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 650

Добавлена в каталог: 09.09.2014

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Предметный указатель

Function, over      170
Functionally complete      38 56
functor      15 113 123 214
Fundamental sequence      375
General model      567
General recursive      303
General variable      92 99
Generalization      315 387
Generalize      79
Generalized Continuum Hypothesis      182 183 198 204 205 607
Generally valid      78 108 315
Generating sign      11 42 214
GENERIC      601
Gentzen, G.      66 68 201 230 286
Goedel numerals      260 388 542 560
Goedel substitution function      271 390 459
Goedel, K.      201 202 203 204 205 274 378 407 508 559 560 600 606 609
Goldbach      564
Goodstein, R.L.      382
Greatest lower bound      192
Greek letters      31 214 230
Greeks      204 609
H $\epsilon$ -model      593
H-disjunction      99 206
H-model      585
H-scheme      100
Halmos, P.R.      205
Hartley Rogers jun.      380
Hausdorf, F.      200
Heine — Borel theorem      546
Held constant      80 83 432
Henkin, L.      559 606
Herbrand, J.      201 378
Hermes, H.      380
Heyting, A.      9 66 378
Hierarchy, analytical      533
Hierarchy, of A-definable sets      409
Hierarchy, of properties      516
Hierarchy, of systems      512 518
Highest degree of unsolvability      329
Hilbert, D.      31 32 67 202 203 205 407 508 606
Hilbert, D. and Ackermann, W.      201 202
Hilbert, D. and Bernays, P.      31 202 205 273 274 508 560 606
Hintikka, K.L.      202
Huntington, E.V.      65 606
Hypersimple set      324 343 379
Hypothesis      39
Idempotent      47 52
Identifiable      37
Identification      127
Identity calculus      372
Identity function      233
Identity relation      170
Ill-formed      6 15
Immediate predecessor      167
Immune set      323
Implication      66
Implication, symbol      427
Implicational propositional calculus      67
Impredicative      77 198 201 511 540 549 559
Improper primary extension      28
Improper subsystem      28
Improper symbol      13 214
inclusion      167
Incomparable degrees      344
Incompleteness      406 508
Incompleteness of A      390
Indecomposable ordinal      210
Independence      36 53 111 120 198 204 462
Independence, proofs      599
INDEX      311 338
Indiscrete      199
Indistinguishable      37
Individual      76
Individual, variable      72 78
Induction      274 423 429 431 438 507 577
Induction formula      8
Induction property      514
Induction theorem      445
Inductive numbers      599
Inequality      213 214 265
Inferior variable      92
Infinite induction      508
Infinite set      177
Infinitesimals      606
Initial function      233
Initial instruction      296
Initial ordinal      180
Initial segment      12 244
Inner model      198 204 600 606
INTEGER      177
Intensional      203 271
Interior      200
Intersection      61 168
Intuitionism      9 66 227 230 286 407 508
Invalid ancestor      397
Inverse      127
Irresolvable statement, $A_{I}$       459 535
Irresolvable statement, A      394
Isomorphic      329 332
Iterator operator      214 508
Jensen, R.B.      204
Jordan, Z.      67
Jump      345
Kalmar,L.      66 202 203 274
Karp, C.R.      559
Kemeny, J.G.      201 606
Kind, of normal numerical term      261
Kind, of ordinal      177
Klaua, D.      382 560
Kleene — Vesley      66
Kleene, S.C.      202 286 289 378 421 560
Kreisel, G.      407
Kronecker, L.      273
Kuratowski, C.      203 421
Lachlan, A.H.      66 274
Lagrange, J.L.      564
Landau, E.      274
Language      1
Last difference      538
Lattice, point      318 409
Lattice, upper semi-      346 380
Laws of algebra      423
Least number operator      245
Least upper bound      192 344 360 545
Lebesgue integral      549 560
Lebesque measure      550 551 552
Left parenthesis      13 42 214
Leibniz, G.W. v      30 65 273 378
Length of a proof      558
Level      440
Leven, F.J.      607
Lewis, C.I.      67
Lexicographic order      94 213
LIMIT      54
Limit, of ordinals      171 546
Limit, point      200
Limited subtraction      237
Limited universal quantification      244
Limited,existential quantification      244
Line, of a diagram      298
Line, of an H-scheme      99
Loeb,M. H.      229 286
Loewenheim, L.      201 202
logical function      133
Lorenzen, P.      201 274 508 559 560
Los, J.      606
Lower formula      19
Lukasiewiez, J.      31 65 66
Lusin,N.      421

MacColl, S.      67
Machover, M.      606
Main formula      42
Many sorted predicate calculus      74 115 520
Many valued model      65 77
Marker      353
Markow, A. A.      31
Mate of a parenthesis      16
Material equivalence      51 213 227 284
Material implication      48 213 227 284 428
Mathematical induction      177 456 508
Matrix      65
Maximal dual ideal      582
Maximal set      366
Meaning      7
Measure,Lebesgue      550 551 552
Membership relation      168 170
meta-language      4 9 40 609
Meta-mathematics      32
Meta-theorem      40
Minimal degree      368
Mixed propositional calculus      34
Modal logic      67
Model      563
Model, basic      37
Model, complete      36 38 76 563
Model, consistent      38 55 113
Model, general      567
Model, standard for arithmetic      565
Model, trivial      37
modus ponens      39 65 66 67 84 114 164 230 396 427 470 484 487 512 517 520 534
Monadic predicate calculus      72 130 202
Moody, E.A.      65
Mostowski, A.      421 560 606 607
Mucnik, A.A.      274 379
Multiplication function      237
Multiplication function, of ordinals      179 210
Multiplicative axiom      181 549
Myhill, J.R.      229 286 379 382
NAME      260 550 599
Natural number      1 175
Natural translation      35
Necessary      67
Negation      29 42 213 227 283 389 508 512
Negation, rule of double      42
Negation, two-valued      29
Negative occurrence      157
Neighbourhood      200
Neumann, J.v      68 203
NEW      5 9 11
Newton, I.      31
Nicod, J.      67
Non-recursively separable sets      364
Non-standard arithmetic      407 408
Non-standard model      403 571 575
Normal class      173 203
Normal class, $\mathscr{J}$ -statement      173
Normal form for ordinals      204
Normal form of a definition      34
Normal forms      64
Normal forms, $\lambda$ -      534
Normal function      262
Normal numerical term      261
Normal proof      92 205
Normal table      296 304 306
Nowhere dense      200
Null class      169 599
Null element      61
Null formula      12
Null sequence      235
Numeral      214
Numeral, Goedel      260
Numerical term      213 214
Object language      4 9
Occurrence      13 21 31
Occurrence, bound      15
Occurrence, free      15
Omission of parentheses      24
One sorted predicate calculus      74
One valued      170
One-one      170
open      19 199
Opposite column      150
Oracle      366 379 553
Order, $A_{00}$ -defined, of a closed numerical term      219
Order, for logical functions      133
Order, of a $\lambda$ -0-reduced function      235
Order, of a constant w.r.t. $\alpha$       578
Order, of a formula      488
Order, of a many-sorted predicate calculus      75
Order, of a predicate calculus      73
Order, of a proof      429
Order, of a table      297
Order, of an H-scheme      100
Order, of predicates      77
Order, of properties      198
Order, of property variables      518 538
Order, standard      586
Order, type      572
Ordered pair      169
Ordinals      175 204
Ordinals, constructive      327
Outer pair of parentheses      14
Overlap      17
pair      169
Pairing function      255
Paradox      201
Parallel axiom      601
Parenthesis      13 16
Parenthesis, omission of      214 215
Parmeter      234
Part, consecutive      12 245
Partial function      291
Partial order      605
Partial recursive      303
Partial, f-calculable      337
Partially calculable      281
Partially calculable, f-calculable      337
Passive, instruction      296
Passive, table      297 378
Peano, G.      30 32 67 202 230 273 508 560
Peirce, E.C.      609
Peripetetics      65
Permutation      42 217
Permutation, recursive      329
Peter, R.      274
Philo of Megara      66
Poincare, H.      201 559
Poles      67
Positive occurrence      157
Possible      67
Post, E.L.      8 65 66 286 378 421 610
Power class      169
Power function      237
Preciseness      1 288
Predecessor      167
Predecessor function      237
Predicate calculus      72 610
Predicate of predicates      73
Predicative      77 198 201 559
Prefix transformations      554
Premiss      7 19
Prenex normal form      91 205
Primary extension      28
Prime ordinal      211
Primitive arithmetic      4 599
Primitive formalization      243
Primitive function      230 233
Primitive recursion      234
Primitive recursively enumerable      284 285

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