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| Kunen K. — Set theory |
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| Предметный указатель |
 , L see "Constructive sets"
-rank 167
 see "Ordinal definable sets"
 165
a.d. see "Almost disjoint families"
Absoluteness 117 125
Absoluteness of defined functions 119
AC see "Axiom of Choice"
Addition, cardinal 28
Addition, ordinal 20
Almost disjoint families 47 87
Almost disjoint families, maximal 47
Almost disjoint families, maximal, sizes of 57 256 286—289
Almost disjoint families, partial order for 55 284
Almost disjoint families, sizes of 290
Antichain 53
atom 237
Axiom of Choice 15
Axiom of Choice, consistency of 162 175
Axiom of Choice, independence of 149 245
Axiom of comprehension 11
Axiom of constructibility 170
Axiom of Constructibility, consistency of 170
Axiom of Constructibility, independence of 203
Axiom of extensionality 10
Axiom of foundation 100
Axiom of Foundation, consistency of 125
Axiom of Foundation, independence of 148
Axiom of infinity 19
Axiom of Infinity, independence of 124
Axiom of pairing 12
Axiom of Power Set 29
Axiom of Power Set, independence of 133
Axiom of replacement 12
Axiom of Replacement, independence of 147
Axiom of union 12
Baire property 240 243
Boolean-valued models 223 234 301—303
Bounded quantifier 118
c.c. see "Chain conditions"
c.c.c. see "Countable chain condition"
c.u.b., Cub 77
Cardinal 28
Cardinal, limit 30
Cardinal, successor 30
Cardinality 27
cf. see "Cofinality"
ch see "Continuum Hypothesis"
Chain 53 68
Chain conditions 212 213 245 see
Chain conditions in iterations 275 291
Chain conditions in products 291—292
class 23
Closed 77
Closed,  -closed 214
Cofinality 32
Collapsing (of cardinals) 205
Compatible 53 69
Complete embeddings 218
Complete ideals and filters 77
Completeness Theorem (Goedel's) 9
Completion 63—64
Condition 52
Consistent 6
Constructible sets 165
Continuum Hypothesis 32
Continuum hypothesis, generalized 32
Continuum Hypothesis, Generalized, consistency of 175 296
Continuum Hypothesis, independence of 209
Countable 28
Countable chain conditions 50 53 see
Countable chain conditions and iterated forcing 271 275
Countable chain conditions in products 51 61 66
Covering Lemma (Jensen's) 267
Definable 153
Definitions, extensions by 22 37
Delta-system 49
Dense 53
Dense,  -dense 240
Dense, dense below 192
Dense, dense embedding 221
df 153
Diagonal intersection 80 91
diamond 80 92
Diamond in 178 181—182
Diamond in generic extensions 227 248 300
Diamond plus 83
Diamond plus in 178 180—182
Diamond plus in generic extensions 249 300
Distributive law 243
Dominating functions 288
Dual (filter or ideal) 76
Easton forcing 262 295
Easton forcing, reverse 277 298
EN 155
Erdoes — Rado theorem 290
Exponentiation, cardinal 31
Exponentiation, ordinal 26
Extension 52
Extensional 105
Filter 53 76
finite 28
Finite axiomatizability 35 46 138
Finitist 7
FN 204 211
Forcing 192
Forcing, language of 194
Formal theory 7
Formalist 7
Formula 3
Fraenkel — Mostowski models 149
Gaps, Hausdorff theorem on 89
GCH see "Continuum Hypothesis Generalized"
GENERIC 186
Height 68
Hereditarily countable 131
Hereditarily finite 131
Hereditary set 9
HT see "Height"
Ideal 76
Inaccessible cardinal 34
Inaccessible cardinal, consistency results 210
Inaccessible cardinal, independence results 133 177
Incompatible 53
Incompleteness Theorem (Goedel's), First 38
Incompleteness Theorem (Goedel's), Second 41
Inconsistent 6
Inconsistent,  -inconsistent 150
Indecomposable ordinal 43
Independent families 257
Independent families, maximal 257
Independent families, maximal, sizes of 258 287
Independent families, sizes of 288
INDEX function 263
| Induction, ordinary 19
Induction, transfinite 25 102
Ineffable Cardinal 182
Infinite 28
Interpretation, relative 8
Isomorphism 14
Iterated forcing construction 273
KH see "Kurepa's Hypothesis"
Koenig's lemma 34 45 69
Kurepa family 75
Kurepa Tree see "Tree Kurepa"
Kurepa's Hypothesis 74
Kurepa's Hypothesis in Levy model 232 294
Kurepa's Hypothesis, independence of 259—262
Lev, level 68
Levy order 231 259
Limit ordinal 18
Loewenheim — Skolem theorem 31 135 156
Logically equivalent 5
Logically valid 5
m.a.d.f. see "Almost disjoint families maximal"
MA see "Martin's Axiom"
Mahlo cardinal 92 247
Martin's Axiom 52 54
Martin's Axiom, consistency of 279
Maximal principle 226
Measure algebra, forcing with 250
Metatheory 7
Minimal 98
Minimal model 182
Model 112
Model, -model 145
Mostowski collapse 105 106
Multiplication, cardinal 28
Multiplication, ordinal 20
NAME 188
Name for a p.o. 269
Name, full 292
Name, nice 208
Natural number 18
Non-atomic 237
Normal Form Theorem (Cantor's) 43
op 191
Ordering, strict 14
Ordering, total 14
Ordering, well- 14
Ordinal 16
Ordinal definable sets 157 300—301
Ordinal, Addition 20
Ordinal, limit 18
Ordinal, Multiplication 20
Ordinal, successor 18
P 286 289
p.o. 186
Partial order 52
Partial order, separative 88
Path 74
Peano postulates 19
Platonist 6
Precaliber 89
Pred 103
Preservation of Cardinals 206 212
Preservation of cofinalities 207 212
Pressing-down Lemma 80
Product order 252
Quasi-disjoint 49
R 95 see
Rado — Milner Paradox 45
Rank 95 104
Rasiowa — Sikorsky Theorem 243
Recursion, Ordinary 27
Recursion, transfinite 25 103
Reduction 218
Reflection theorem 136 137
Regular 33
Relativization 112 141
Relativization of defined notions 114—116 142
Root 49
Russell paradox 10
S see "Successor function"
Saturated ideals 93
Saturated ideals, consistency of 250
Schroeder — Bernstein theorem 27 43
Scope 4
Sentence 4
Separable 50 86
Separative 88
Set-like 102
sh see "Suslin's Hypothesis"
Singular cardinal's problem 296—297
Skolem, function 139
Skolem, Paradox 141
Solovay's Lemma 287
Stationary sets 78
Stationary sets in generic extensions 247 250
Sub-tree 68
Subformula 4
Successor, function 18
Successor, ordinal 18
Support 273
supt 273
Suslin, algebra 243
Suslin, Hypothesis 66
Suslin, line 66
tr cl see "Transitive closure"
Transitive 16
Transitive closure 99
TREE 68
Tree, Aronszajn 69
Tree, Aronszajn, special 91
Tree, complete (binary or I-ary) 68
Tree, ever-branching 81
Tree, Kurepa 74 see
Tree, product 90
Tree, Suslin 69 229 see
Tree, Suslin, Jech order for 248—249
Tree, well-pruned 71
Truth value 224
TYPE 18
Ulam Matrix 79
Ultrafilters 289
Uncountable 28
Universal closure 5
UP 191
Val 189
Variable 3
Variable, bound 4
Variable, free 4
Weakly compact cardinal 92 297
Well-founded relations 98 102
Well-founded sets 95
WF see "Well-founded sets"
Zermelo set theory 147
ZF,  , ZF-P, etc. vi
Zorn's lemma 44
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