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

Abbreviation      23
Abel, N.H.      560
abstract      15
Abstraction, function forming      213
Abstraction, of variable      16
Abstraction, operator      214
Abstraction, symbol      13
Ackermann, W.      201 202 233 275
Addison, J.W.      421 560 606
Addition, cardinal      181
Addition, function      236
Addition, ordinal      179
Aleph      181 204 604
Algebraic closure      377
Algorithm      273 378 609
Alphabet      158
Alphabetical order      27
Analysis      548
Analytical hierarchy      553
Anderson, J.M.      66
Anti-system      228 286
Antinomy, of greatest ordinal      176
Antinomy, of liar      31
Application      15 213
Applied predicate calculus      73
Applied propositional calculus      34
Arabs      273 609
Argument      15
Aristotle      30 65 609 610
Arithmetic, degree      416
Arithmetic, set      346
Arithmetically, defined      416
Arithmetically, undefinable      416 417
Arithmetization of syntax      274
Array      324
Association to the left      14
Associativity, of conjunction      45
Associativity, of disjunction      43 47 52
atomic      293
Available      107
Axiom scheme      19
Axiom, of choice      181 183 198 204 205 555
Axiom, of constructivity      602 607
Axiom, of infinity      175 203 204 598
Axiom, of reduction      203
Axiomatizable      372 403
Axioms, of $A^{(K)\ast}$       519
Axioms, of $A^{(K)}$       518
Axioms, of $A_{00}$       215—216
Axioms, of $A_{0}$       278
Axioms, of $A_{1}$       438
Axioms, of A      387
Axioms, of A'      513
Axioms, of Boolean algebra      62
Axioms, of E      430
Axioms, of set theory      171
Axioms, of the classical predicate calculus      78
Axioms, of the classical propositional calculus      42
Bachmann, H.      204
Bar-Hillel, Y.      205
Barwise, J.      559
Base      20
Based on      74 114 406
Basic formal system      398
Basic propositional calculus      37
batch      572
Behmann, H.      202
Bernays, P.      31 65 66 67
Bernstein, F.      204
Beth, E.W.      202
Biconditional      51
Binary predicate calculus      166 203
Bochenski, L.M.      65
Boethius      65
Bolzano — Wierstrass      377
Boole, G.      30 65 66 68
Boolean algebra      61 66 68 70 71 129 194 605
Boolean ring      71
Boolean valued model      194 204
Borel, E.      421
Bound occurrence      14 267
Boundary      200
Bounded truth-table      381
Branch      20
Brouwer, L.E.J.      8 9 66 273
Building rules      42 78 217
Calculable      130 232 246 258
Caley, A.      205
Cancellation      44 78
Cantor, G.      203 204 274 380 407 559
Cardinal, integers      180
Cardinal, numbers      180
Carried forward      443
Cases, definition by      243
Categorical      564
Cauchy, A.      560
Chain of degrees      374
Change of bound variable      23
Characterise      577 606
Characteristic function      243
characteristica universalis      30
Choice function      162
Chrysippus      65
Church's thesis      288 343 378
Church, A.      31 65 66 68 202 203 230 273 286 378 379 606 609
Chwistek, L.      203
Class, existence      516
Class, of ordinals      180
Class, proper      169
Class, theory      65 168
Class, variable      516
Classical predicate calculus      78
Classical propositional calculus      42
Closed, set      199
Closed, statement      267
Closure      80 84 574
Cohen, P.      204 599 609
Cohesive set      365 379
Collision of bound variables      198
Combinatory logic      230 378
Commutativity, of conjunction      45
Commutativity, of disjunction      43 47 52
Compact      200
Complement      61 168 192
Complete arithmetic      213
Complete Boolean Algebra      192 605
Complete degree      345 356 360
Complete set      323 343 379 381
Complete set of atomic instructions      294
Complete table      295
Complete w.r.t. negation      30 227 315
Complete w.r.t. truth-definition      29 225 280
Completely productive set      335
Completeness, of $\mathscr{P}_{C}$       55
Completeness, of higher order predicate calculi      594
Complex number      178 548
complexity      191
composition      42
Compound quantifier      73
compound statement      213
Comprehension axiom      516
Computing degrees of unsolvability      419
Concatination sign      11 31 215
Concept writing      30
Conclusion      7 19
Conditional symbol      48
conditions      601
Conjunction symbol      45 214 265
Conjunctive normal form      56 64 68 81
Connected table      300

Connective      6 34
Consecutive part      12
Consequence      18
Consistency      55 113 224 398 407 451 501 519 530
Consistent, model      113
Consistent, w.r.t. negation      30 113 227
Consistent, w.r.t. truth-definition      29 213 224 280
Constant      13 72
Constant, function      233
Constructable universe      204
Construction sequence      234 568
Constructive method      6 27
Constructive ordinals      327 511
Continuum Hypothesis      182 204 205 406
Contraction of quantifiers      409
Contributing table      325
Convergence function      375
Converse relation      170
Conversion $\lambda$       230 378
Coordinate function      236 242
correctness      1
Correspondence, (1-1)      180
Corresponding column      150
Corresponding occurrence      21
Corresponding parenthesis      16
Corresponding set      582
Countable chain condition      193
Counter example      149
Course of values recursion      247 434
Cover      200
Craig, W.      202 408
Creative set      327 343 379
Crossley, J.N.      607
Curry, H.B.      230
Cut formula      49 see
Davis, M.      380
De Morgan, A.      30 66 67 609
De Morgan, laws      47 52
Decidability of $\mathscr{P}_{C}$       57
Decidable      27 213 227 229
Decidable, arithmetic      225
Decomposable      210
Dedekind induction      273 274
Dedekind sections      178 376
Dedekind, finite      603
Deduction Theorem      48 80 115 231 469 521
Deductive method      7 39
Definable, $A_{00}$       232 389
Definable, $A_{0}$       399
Definable, A      409 557
Definition      23 34
Definition, by cases      243
Degree, of solvability      344
Degree, of unsolvability      329 343 607
Dekker, J.E.      379 382 408
Denumerable model      110 204
Denumerable ordinals      180
Derivation      40
Derived rule      20 123
Descartes, R.      213
descendent      79 578
Designated      36 76 564
Destruction rules      228
Detachment      49 see
determine      218
Diadic predicate calculus      73
Diagram of a table      298
Dilution      42 78 217
Dilution, existential      278
Direct product      127 170
Discrete      199 324
Disjoint      193
Disjunction      42 214 265
Disjunctive normal form      56 64 68
Distributive laws      43 47 52 86 193
Domain      170
Domain, restricted      170
Dorp, J.      66
Double Negation      42 47 52
Double nested recursion      256
Double recursion      250 434
Dual      53 90
Duality      52
Duerr, K.      65
E-correct      438 455
Effective truth definition      29
Effectiveness      32 66 273
Element of a model      36
Elimination, of $\epsilon$ -symbol      184 205
Elimination, of axiom schemes      126
Empty set      167
End segment      12 244
Enumerable      284
Enumerating function      262 341
Enumeration of primitive recursive functions      260
Epimenides      31
Equality      119 123 166 171 213 214 265
Equation calculus      430
Equivalence relation      123
Equivalent      28 35 37 51 235 262 281 300 304 312
Eratosthenes      273
Essentially undecidable      314 315 316 379 431
Euclid      203 273 601
Excluded Middle      see "T.N.D."
Exclusiveness      219
Existential dilution      78
Existential quantifier      78 116 278
Existential statement      282 499
Exponentiation, function      237
Exponentiation, of cardinals      181
Exponentiation, of ordinals      179 211
Express      48 51 329
Extension, of $A^{(K)}$       541
Extension, of A      425
Extension, of a formal system      28
Extensional      171 203 271
f-calculable      337
f-column      150
Factorial function      237
False ancestor      472
Falsity definition      29 213 219 272 283 389
Field      413
Finite, Dedekind      603
Finite, set      177 603
Finiteness      66
First Order Predicate Calculus      78
Fitch, F.B.      229 407
Fixed point proposition      335 379
Forcing method      204 601
Forcing rules      601
Formal system      10 27 28 378 428 438 609
Formalization of primitive recursion theory      243
Formation rules      15
Formula, forms      21 22
Formula, induction      8 9
Fraenkel, A.      204 205
free      354
Free, disjunctive form      115
Free, for      16 23
Free, occurrence      14
Free, variable      15 72
Frege, G.      30 32 65 66 67 201 203
Freundental, H.      9
Friedberg, R.M.      274 379
Fubonacci      273
Full model      567
Function      76 170 215
Function, calculus      72
Function, characteristic      266
Function, of a complex variable      548

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