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

Primitive sign      10
Principal characteristic function      244
Principia Mathematica      8 30 203 205
Principle of Mathematical Induction      423
Priority, list      353
Priority, method      274 379
Problem, decision      66 130
Problem, of formalizing      38
Problem, Post's      352
Problem, reduction      136 202
Procedure, rules of      19
Produces      311
Product, function      239
Product, of a table      312
Product, of ordinals      210
Product, of relations      170
Production, a level      441
Production, function      239
Production, Post      378
Productive set      330 379 405
Productive, completely      335
Progression      1 8
Projection of a set      346
proof      20
Proof, $A_{00}$       265
Proof, $A_{I}$       451
Proof, in normal form      92
Proof-predicate      265 390 448
Proof-thread      20 31
Proof-tree      20
Proper class      169
Proper symbol      13
Property      278
Property, induction      514
Property, variable      511
Propositional calculus      31 34 610
Pure iteration      254 257
Pure predicate calculus      78
Pure propositional calculus      42
Quantificational power      157
Quantifier      72 201 213
Quantifier, compound      73
Quantifier, existential      278
Quantifier, limited      244
Quantifier, simple      73
Quantifier, universal      387
Quine, W.vO.      9 31 275
Quotient      240
Ramified types      77 198 559
Ramsey, P.F.      203
RANGE      170
Rank, of a proof      93
Rank, of a term      219
Rational numbers      178 375
Real numbers      178
Recursion, course of values      247 434
Recursion, double      250
Recursion, simple nested      252 434
Recursion, simultaneous      247 434
Recursion, with substitution in parameter      248 434
Recursive fundamental sequence      375
Recursive ordinals      328
Recursive permutation      329
Recursive real numbers      375 544
Recursive statements      254
Recursive, degree      344
Recursively decidable      314
Recursively enumerable      319 322 345
Recursively independant      361
Reduced prefix      554
Reduced, $\lambda$ -0-      234
Reducible,(1-1)      331 380
Reduction, problem      136 202
Reduction, type      142
Redundant      120
Reflexive      123
register      338 358
Regularity      51 88 498
Related occurrences      21
Relation      123 168 170 609
Relative consistency proof      600
Relativization      169
Relevant table      325
Remainder, of an ordinal      210
Remainder, on division      241
Remodelling rules      42 78 217 228
Represented      235 311 337
Resolved $\mathscr{F}_{C}$       160
Resolved form      166 206
Restricted      79 92 99
Restricted quantifier      244
Reversibility, Ia, b, IIb, c, e      79 163
Reversibility, Ia, IIb, c      43
Reversibility, IIb'      45
Reversibility, IIb, c, e      163
Reversibility, IId*      98
Reversibility, in $A^{(K)}$       519
Reversibility, in $A_{I}$       463
Rice, H.G.      382
Riemann integral      548
Right parenthesis      13 42 214
Ring      412
Ring, boolean      70
Robinson, A.      606
Robinson, R.M.      247
Rogers,H. jun.      380 508
Romans      609
Rose, G.F.      379
Rosser, J.B.      204 205 286 559 560 607
Rowbottom, F.      230 274
Rule      10 13
Rule, $A_{00}$       213
Rule, $\lambda$ -      22
Rule, of consequence      18
Rule, of formation      14
Rule, of predicate calculus      78
Rule, of procedure      19 217
Rule, of propositional calculus      42
Rule-scheme      20
Russell, B.      8 9 31 32 67 201 559 606
Ryll-Nardzewski, C.      606
S-model      580
Sacks, G.      379 607
Satisfaction      101 108 141 201 568 570 590
Satisfiable over      109 567
Scheme, of generation      11
Scheme, of primitive recursion      234
Scheme, of substitution      233
Schmidt, A.      201
Schoenfinkel, M.      202
Scholastic logic      65
Scholz, H.      203
Schroeder, E.      30 65 67 201 202 286
Schuette, K.      66 201 202 508
Scope of an abstraction      16
Scott, D.      204
Secondary extension      28
Secondary formula      42
Segment, end      244
Segment, initial      244
Segment, of an ordinal      210
Semantic tableau      149 206
Semi-formal system      508
Semi-lattice      346
Semi-model      77
Sentential power      157
Separable      200
Sequence, C      568
Sequence, of degrees      261
Sequence, of natura numbers      235

Sequence, S      568
Sequenzen      68
Set      169
Set theory      171
Set variable      169
Sheffer, H.M.      68
Sheperdson, J.C.      204 607
Shoenfeld, J.R.      379 382 508
Sierpinski, W.      204 205
SIGN      5 10 213
Sikorski, R.      205
Similar      177
Similarity relation      177
Simple nested recursion      252 434
Simple quantifiers      73
Simple set      323 343 379 610
Simply connected      548
Simultaneous recursion      247 434
Simultaneous satisfaction      589
Singularly predicate calculus      65 208
Situation      307
Skolem, S-normal form      138 140
Skolem, Th.      201 202 204 205 207 273 274 408 599 606
Skolem, V-normal form      138 140
Skolimowski, H.      67
Smullyan, R.M.      378 382
Solovay, R.      204
solvable      130 132
Specker, E.      382
Spector, C.      379 560
Spectrum      372
Square      10 288
Square-root function      254
Standard, determination      220
Standard, model      403 565
Standard, order      586
Standard, position      294
Standard, proof      220
Standard, truth definition      563
State      366
Statement      19 214 266
Statement-form      22
STATUS      14
Stoic — Megara school      65
Sub-system      28
Subsidiary      42
Substitution, function      271
Substitution, in parameter      248 434
Substitution, rule      67 114 163
Substitution, scheme      233
Subtraction, limited      237
Successor function      213 214 230 233
Sum of ordinals      210
Summation function      239
Superior variable      92
Suppes, P.      205
Suranyi, L.      202 203
Sylvester, J.J.      66
Symbol      10 213
Symmetry      123
Syntax      7
Syntax, language      31
System, $A^{(K)\ast}$       519
System, $A^{(K)}$       518
System, $A_{00}$       213
System, $A_{0}$       278
System, $A_{I}$       438
System, $\mathscr{F}_{C}$       42
System, $\mathscr{P}_{C}$       78
System, A      387
System, A'      511
System, E      430
Syzygy      55 66
t-column      150
Table, complete      295
Table, model      37
Table, truth      58 66
Tableau, semantic      149
tally      4 292
Tape      5 9 288 378
Tarski, A.      9 31 65 201 202 286 379 407 421 559 606
Tautologous      92
Tautology      55 64 66 101 102 104 105 106 521
Term      266
Term, numerical      213 214
Terminating instruction      296
Tertium non datur (T.N.D.)      9 66 80 91 396 461 517 520
Theorem, induction      49 85 445
Theorem, scheme      20
Theory      114
Theory, degree of      372
Theory, in free disjunctive form      115 121
Thread of a proof      429
Three-valued propositional calculus      65
topology      199
Total function      303
Transfinite induction      178
Transfinite induction, jump      416
Transfinite induction, number      175 598
transform      170
Transitivity      123
Translation      116 124
Treated      157 441
Tree-form      20
Trivial model      37
TRUE      6
Truth      6
Truth, -definition      29 31 193 272 279 282 388 395 401 405 416 420 521 535 538
Truth, table      58 66
Truth, values      55
Turing, A.M.      9 31 233 273 378 559 609
Turing, machine      130 288
Turing, oracle      336
Two-valued model      564
Two-valued negation      29
TYPE      13 14 15 17 18
Type, ramified      77 198 559
Type, symbol      34
Type, theory      31 203
Ullian, J.S.      379
Ultra filter      582
Ultra filter, product      589
Unbounded least number operator      273 284
Unbounded quantifier      273 387 407 438
Unbounded truth tables      381
Uncertainty principle      551
Undecidability, essential      379 391 508
Undecidability, of $\mathscr{F}_{C}$       314
Undecidability, various results      316
Undefinable arithmetically      416 417
Undesignated      76 564
Uniformly effective      322
Union class      61 127 168 169
Unit class      169
Unit, element      61
Universal algorithm      273
UNIVERSAL class      169
Universal function      291 313
Universal quantifier      89 387 407 438
Universal statement      389 484
Unlimited least number operator      273 284
Unlimited quantifier      273
Unsolvability, degree of      329 343 379 607
Upper formula      19
Upper semi-lattice      344
Vacant      354
Val      522
Valid, M-      37
Valid, over a general model      567
Validity      108 193 201

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