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| Hinman P.G. — Fundamentals of Mathematical Logic |
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| Предметный указатель |
Consistent 6 44 96 187
Consistent formula 680
Consistent in a theory 680
Consistent proof 210
Consistent theory 7 143 187 191
Consistent,  - 64 217
Consistent,  - 379
Consistent, finitely 47 194
Consistent, maximal 46 143
Constant function 328
Constant symbols 4 86
Constant symbols of type  290
Constant term 176
Constant, arbitrary 175
Constants, extension by 173
Constructible from a 574
Construction 63
Constructive 314
Contagiously incomplete 444
Contagiously undecidable 444
continuous 629
Continuum Hypothesis 456 466 514 547 624 636 653 686
Continuum hypothesis, generalized 283 298 514 700
Contradiction 34
Contraposition 34
Correctly 764 786 793 800
Correctly, very 790 802
Correctness function 788
Correctness Lemma 764
Correctness Lemma for  805
Correctness Lemma for  ength 801
Correctness Lemma for Length 786
Countable 485 512
Countable axiom of choice 526
Countable chain condition 591
Countable Compactness Theorem 194 215 221 229 407 687
Countable Completeness Theorem 210 210 221 229 407 554
Countable Craig Interpolation Theorem 223
Countable Downward Loewenheim — Skolem Theorem 127
Countable induction system 287
Countable language 94
Countable Model Existence Theorem 221 222
Countable partial ordering 752 768
Countable Robinson Interpolation Theorem 222 699
Countable structure 118 289
Countable union 520
Countable Vaught Test 147
Countable well-ordering 279 625 641
Countably complete 620
Countably universal 690 692
Course-of-values recursion 336 484
Craig interpolant 224 267
Craig Interpolation Theorem 267
Creative 756
Cumulative hierarchy 467
Cut 34
d.r.e. 772 778
De Morgan's laws 34
Decidability 359
Decidable 7 55 112 312 326
Decidable set of formulas 355
Decidable theory 8 146 181 188 191 202 248 311 359
Decidably axiomatizable 8 61 141 146 202 311 313
Decision procedure 55
Dedekind cuts 127 487
Dedekind finite 512
Dedekind infinite 512
Dedekind, R. 161
Deducible 206
Deduction system,  - 300
Deduction system, effective 286
Deduction Theorem 210 216
Definability Beth's Theorem 267 271 700
Definability Hypothesis 313
Definability Theorem 365
Definable 400 567
Definable explicitly 267
Definable from parameters 128
Definable implicitly 267 433
Definable ordinal 576
Definable over a structure 128 312 364 400 403
Definable relation 157 159
Definable set 163 173
defined 347
Defined on names 584
definite 382
Definition by cases 333
Definition by generalized recursion 26
Definition by recursion 25
Definition inductive 21 488
Definition, extension by 178
Definition, pseudo- 182
Definitional extension 178
Degree, many-one 351 734
Degree, r.e. many-one 736
Degree, r.e. Turing 763 773
Degree, relatively r.e. 770 773
Degree, truth-table 753
Degree, Turing 758
Denial of the antecedent 34
Dense below 597
Dense linear ordering 84 154 170 201 685
Dense linear ordering, complete 280
Dense set of conditions 579
Density, lower 791
Denumerable 485
Denumerable language 94
Denumerable structure 118
Dependence property, finite 725
Derivability conditions 423
Derivation,  - 23
Descriptive set theory 630
Destroyed 764
Determined 623
Diagonal argument 319 413
Diagonal intersection 524
Diagonal Lemma 320
Diagonal set 320
Diagonally non-recursive (DNR) 769
Difference of r.e. sets 772
Digital computer 437
DIMENSION 139
Diophantine 400
Direct product 130 133
Discrete ordering 134
Disjoint 677
Disjunction 16 293
Disjunctive normal form 37 110
Disjunctive syllogism 34
Distinctive 283
Distinguished elements 83 91
Distributive law 34 75 99
divides 334
Division lemma 508
Domain 473
Domain over A 290
Dominated 363
Dot convention 4 86 179 459 464
Double Negation 34
Downward Morley Theorem 710
Downward persistent 123 145
Downward persistent,  - 252
Dyadic rationals 134
Effective deduction system 286
Effective language 95 112
Effective logic 730
Effective procedure 54
Effective semi-procedure 58
Effectively calculable 55 326
Effectively enumerable 58 202 318
| Effectively equivalent logics 730
Effectively jump codes 795
Effectively regular 731
Effectively translates 730
Ehrenfeucht — Mostowski theorem 717
Ehrenfeucht's Theorem 668 671
Element- 541
Elementarily closed 235
Elementarily embeddable 130
Elementarily equivalent 116
Elementarily prime model 258 690
Elementary chain 134
Elementary embedding 130
Elementary equivalence of structures 116
Elementary extension 125
Elementary substructure 125 553
Elementary type 657
Elimination of quantifiers 147 157 167 256 258 312 393
Elimination to 52
Embeddable 124
Embeddable elementarily 130
Embeddable partially - 664
Embeddable, - 241
Embedding 124
Embedding, - 241
Embedding, elementary 130
Embedding, partial 158 292 656
Embedding, partial  - 665
Embedding, partial - 655
Embedding, partial  - 656
Embedding, partial elementary 656
Empty class 458
Empty set 90
End extension 374 570
Enumerability theorem 146 193 202 215 285 312 362
Enumerability Theorem, Propositional 60
Enumerable computably 340
Enumerable effectively 58
Enumerable recursively 342 349 377
Enumerates 342
Enumeration stage 741
Enumeration validity 731
Equality Axioms 98 112 113 205 361
Equality symbol 86 92
Equality, language of 86 149 359
Equational language 432
Equationally derivable 435
Equationally implicit 433
Equipotency class 515
Equipotent 485 510
Equivalence relation 477
Equivalence, many-one 350
Equivalent logics 723 730
Equivalent, elementarily 116
Equivalent, logically 96 109 112 229
Equivalent, many-one 350 734
Equivalent, tautologically 32 51 75 97
Equivalent, Turing 758
Essentially undecidable 444
Euclid 8 309 334
Eventually periodic 173
Exchange property 139
Excluded Middle 34
Existential closure 109
Existential formula 122 401
Existential quantifier 86 100
Existential quantifier axioms 206 299 360
Existential quantifier rule 206 299 360
Existential second-order formula 280
Existential, logically 122
Existential, simply 260
Existential, simply - 148
Existentially axiomatizable 144
Existentially closed 257
Exists unique 177
expansion 34 174
Explicitly definable 267
Explicitly definable, weakly 271
Exportation 34
Expression 14 87
Extendable 591 664
Extended Countable Model Existence Theorem 222
Extended First Incompleteness Theorem 319
Extension 119
Extension by constants 173
Extension by definitions 178 426
Extension by pseudo-definitions 182
Extension elementary 125
Extension end 374 570
Extension finite 63
Extension forward 158 658
Extension language 173
Extension signature 722
Extension, - 241
Extension, -inessential 701
Extension, backward 158 658
Extension, complete 45 156
Extension, conservative 180
Extension, inessential 701
Extension, Skolem 185
Extensional 564 616
Extensionality 90 456
Factorial 330
Faithfully interpretable 188 444
False in a structure 102
False, logically 103
False, tautologically 32
Falsity 33 103
Fibonacci sequence 336
Field 85 132 145 251 447
Field of a relation 474
Field of sets 74
Field, algebraically closed 247 697
Field, real closed 248
Filter 68 77 579
Filter generated 70
Finitary 36
Finitary Closure Recursion Theorem 494
Finitary Fixed-point Thm 491
Finitary function 21 327 489
Finitary function closure oper. 489
Finitary induction system 287
Finitary set operation 491
finite 272 485 496
Finite character 24 269
Finite dependence property 725
Finite extension 63
Finite function 579
Finite hereditarily 56 494
Finite injury 798
Finite intersection property 69 78
Finite language 94
Finite Ramsey's Theorem 54
Finite sequence 334 486
Finite structure 118 175 289
Finite validity 450
Finite, Dedekind 512
Finitely axiomatizable 57 141 203 250 547
Finitely consistent 47 194
Finitely generated 24 235
First Extension Lemma 245
First incompleteness theorem 10 318 376 384 389 444 737
First Incompleteness Theorem for ZF 483
First Incompleteness Theorem, Extended 319
First Modesty Theorem 709
First Quantifier Elimination Theorem 259
First Use Theorem 760
First-order language 86 550
First-order logic 83 727 731
First-order, closed 661
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