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| Tourlakis G.J. — Lectures in Logic and Set Theory: Set Theory |
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| Предметный указатель |
GENERIC 518
Generic Extension 524 526
Global choice see "AC"
Goedel operations 396
Goedel — Rosser incompleteness theorem 92
Goedel's second incompleteness theorem 93
Goedel, K. 3 6 229 395 467
Gries, D. 5
Ground model 518 526
Hausdorff's theorem 230 357
Hausdorff, F. 230
Hermes, H. 43
Heyting, A. 4
Hilbert, D. 4 12 42 93 315
Hinman, P.G. 498
Hypersets 156 368
I.H. 23
i.p. 25 497
i.p.s. 497
IC 293
IFF 13
Image 177
Image of a class under a relation 196
Immediate predecessor set 497
Immediate predecessors 25 497
Implied multiplication 260
Imported constant 55
Inaccessible 483
Incompatible 520
Incompletable 89
Incompletableness 62 87
Incompleteness 6
Incompleteness theorem (first, of Goedel) 112
Indefinite article 75
Index class 193
Indexed family of sets see "Family of sets"
Individual variables 9
Induced order 319
Induction 235
Induction hypothesis 23 235
Induction on finite sets 441
Induction on TC 393
Induction on WR-finite sets 441
Induction over  438
Induction over  343
Induction over  235
Induction over , course-of-values 281
Induction over On 343 344
Inductive definitions 19 21 see
Inductive set see "Set"
Inductiveness condition 293
Infima 347
Infimum 347
Infinite descending chain 297
Infix 14 195
Informal 10
Initial ordinals 459
Injection see "Function injective"
Injective function see "Function"
Input object 193
Instance 37 129
Interpretation 54
Interpretation function 525
Intersection 153
Intersection of a class 153
Intersection of a family of sets 153
Intersection of a higher order collection 193
Intersection of many classes 142
Intersection of two classes 141
Inverse image of a class under a relation 196
Iota notation 73
Irreflexive 284
Isomorphic 240
Isomorphic image 242
Isomorphism 241 313 316
Iteratively 22
Jech, T.J. 229 395
Kamke, E. 355
kp 192
KPU 192
Kronecker, L. 5
Kuratowski — Zorn theorem 230 356
Language, countable 64
Language, extension 55
Language, first order 16
Language, restriction 55
Language, uncountable 64
Lattice 521
Laws of exponents see "Relation positive
Least number principle 281
Left inverse see "Function"
Leibniz rule 52
Leibniz, G.W. 35
Levy, A. 199 228 439 447 467
Lexicographically 91 413
Limit cardinal 465 555
Limit ordinal 342
Lindemann, F. 5
Linear order see "Order"
Linearly ordered class 287
Linearly ordered set 230 287
LO class see "Linearly ordered class"
LO set see "Linearly ordered set"
Loewenheim, L. 64
Logical symbols 9
Logically implies 54
Lower bound, greatest 347
m-based rule class 503
M-generic sets 522
Mal'cev, A.I. 65
Manin, Yu.I. 40
Material implication 17
Mathematical theory see "Theory"
Matrix multiplication 283
Maximal element 287
Maximum element 287
Mc 289
MC, weak 372
Metalanguage 7
Metamathematics 7
Metatheorems 11
Metatheory 4 7
Metavariable 169
Minimal condition 289
Minimal element 287
Minimality principle 239
Minimum element 287
Model 57
Model, countable 64
Model, uncountable 64
modus ponens 37 120
Monotonicity 51 531
Montague, R. 306
Moschovakis, Y.N. 186 502
Moss, L. 368
Mostowski, A. 310 426
MP 37
Multiplication of natural numbers 259 282
Multiplication of natural numbers, is associative 282
Multiplication of natural numbers, is commutative 282
n-vector 185
Natural numbers 12 235
Natural numbers, distributive law 282
Natural projection 280
Non-deterministic 498
Non-extensional 312
Non-monomorphic 498
Non-null 141
Non-void 141
normal 349
| Notion of forcing 520
NULL 141
Numeral 42 88
object variables 9
Occurrence 13
Occurs in 13
One point rule 71 201
One-to-one function see "Function"
Onto 64
open 520
Operator 437
Operator, inductive 438
Operator, monotone 437
Order 284
Order isomorphism 317
Order of x 397
Order type 241 339
Order, lexicographic 224
Order, linear 287
Order, partial 284
Order, total 287
Order-isomorphic 317
Order-preserving 348
Ordered disjoint sum 412
Ordered n-tuple 185
Ordered pair 184 188
Ordered sequence 20
Ordinal 324 331
Ordinal exponentiation 423
Ordinal number 43 324 331
Ordinal of a monotone operator 503
Ordinal, cofinal in 478
Ordinal, limit 342
Ordinal, regular 479
Ordinal, singular 479
Ordinal, successor 342
Ordinals 65 219 284 324
Ordinary recursion theory 196
Output object 193
Pairing function 184 186
Pairing function, first projection of 186
Pairing function, second projection of 186
Pairwise disjoint 216
Pairwise disjoint sets or classes 153
Paradoxes 104
PARAMETER 137 170 194
Parsable 30
parse 22
Partial function see "Function"
Partial multiple-valued function 199
Partial order see "Order"
Partially ordered class 286
Partially ordered set 286
Partition 278
Peano arithmetic 87 101
Pigeon-hole principle 432
Pincus, D. 468
Platonist 103
PO class see "Partially ordered class"
PO set see "Partially ordered set"
Post's theorem 97
Post, E. 97
Power class 178
Power set 149 178
Predecessor 238 498
Predicate 10
Predicate, defined, subset see "Subset relation"
Prefix 13 195
Preservation of Cardinals 555
Prime factorization theorem 446
Primitive recursive pairing function 189
Principle 3 of set construction 161
Priority 17 533
Priority of set operations 154
PRODUCT 485
Programming formalism 233
Programming language 233
proof 1 38
Proof by auxiliary constant 53
Proof by cases 52
Proof by contradiction 51
Proper class see "Class"
Proper extension 520
Proper prefix 13
Proper subset see "Subset relation"
Propositional axioms 97
Propositional calculus 97
Propositional connectives 9
Propositional logic 97
Propositional segment 97
Propositional valuations 30
Propositional variable 29
Provably equivalent 43
Proved from 38
Pure recursion 308
Pure recursion over 344
Pure recursion over On 344
Pure sets 310 346
Pure theory 57
Quantifier bounded 149
Quotient set 277
R-induction 496
Rank 369
Rasiowa, H. 42
Recursion 20
Recursion over 344
Recursion over On 343
RECURSIVE 89
recursive definitions 21 244 301
Recursive definitions over 244
Recursively axiomatizable 40
Recursively axiomatized 39
Reference set 145
Reflection principle 504
Reflexive closure 262
Reflexive-transitive closure 362
Regularity axiom see "Axiom nonlogical"
Relation 20 194 see
Relation, antisymmetric 260
Relation, binary 194
Relation, closure 262 495
Relation, closure, reflexive 262
Relation, closure, symmetric 262
Relation, closure, transitive 262
Relation, composition 253
Relation, converse of 196
Relation, defining formula of 194
Relation, diagonal 257
Relation, domain of 195
Relation, equivalence 276
Relation, extension of 198
Relation, field of 195
Relation, identity 257
Relation, input of 195
Relation, inverse of 196
Relation, irreflexive 260
Relation, left field of 196
Relation, left-narrow 301
Relation, n-ary 194
Relation, nontotal 196
Relation, onto 196
Relation, output of 195
Relation, positive power of 256
Relation, positive power of, laws of exponents 259
Relation, range of 195
Relation, reflexive 260
Relation, restriction of 198
Relation, right field of 196
Relation, setlike 301
Relation, single-valued 199
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