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Kunen K. — Set theory
Kunen K. — Set theory

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Название: Set theory

Автор: Kunen K.

Аннотация:

Many branches of abstract mathematics have been affected by the modern independence proofs in set theory. This book provides an introduction to relative consistency proofs in axiomatic set theory, and is intended to be used as a text in beginning graduate courses in that subject. It is hoped that this treatment will make the subject accessible to those mathematicians whose research is sensitive to axiomatics. The readers should have had the equivalent of an undergraduate course on cardinals and ordinals, but no specific training in logic is necessary.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 328

Добавлена в каталог: 24.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbf{L}$, L      see "Constructive sets"
$\mathbf{L}$-rank      167
$\mathbf{OD}$      see "Ordinal definable sets"
$\mathscr{D}$      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, $\lambda$-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, $\kappa$-dense      240
Dense, dense below      192
Dense, dense embedding      221
df      153
Diagonal intersection      80 91
diamond      80 92
Diamond in $\mathbf{L}$      178 181—182
Diamond in generic extensions      227 248 300
Diamond plus      83
Diamond plus in $\mathbf{L}$      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, $\omega$-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, $\omega$-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, $ZF^{-}$, ZF-P, etc.      vi
Zorn's lemma      44
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