Hrbacek K., Jech T. — Introduction to Set Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Hrbacek K., Jech T. — Introduction to Set Theory

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Название: Introduction to Set Theory

Авторы: Hrbacek K., Jech T.

Аннотация:

Revised edition intended as a primary text for mathematics courses. Basic material covered includes: relations, functions, and orderings; finite, countable, and uncountable sets; and cardinal and ordinal numbers. Advanced material discussed includes the Axiom of Choice, filters, ultrafilters, closed unbounded and stationary sets, partitions, large and measurable cardinals, well-founded and non- well-founded sets, partition calculus, and other topics.

Язык:

Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-rd Edition, Revised and Expanded

Год издания: 1999

Количество страниц: 291

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\Delta$ -lemma      211
$\sigma$ -additive      150 151 241
$\sigma$ -algebra      151
$\sigma$ -complete filter      246
Absolute      273
Accumulation point      184
Addition      52 172 176
Addition of cardinal numbers      93
Addition of ordinal numbers      119
Additive function      147
Aleph      131
Aleph naught $\aleph_0$       78
Algebraic number      101
Almost disjoint functions      213
Analytic set      278
Antichain      225 237
Antisymmetric relation      33
Aronszajn tree      228
Associativity      13 94 122 159 160
Asymmetric relation      33
At most countable      74
atom      244
Atom less measure      244
Automorphism      60
Axiom of Anti-Foundation      262
Axiom of Constnictibility      273
Axiom of Countable Choice      144 152
Axiom of Existence      7
Axiom of extensionality      7
Axiom of foundation      259
Axiom of infinity      41
Axiom of Pair      9
Axiom of Power Set      10
Axiom of regularity      259
Axiom of union      9
Axiom of Universality      265
Axiom Schema of Comprehension      8
Axiom Schema of Replacement      112
Axioms      3
Baire function      200
Banach, Stefan      149
Basis      146
Beth      223
Binary operation      55
Binary relation      19
Bisimulation      263
Borel set      194
Bounded sequence      181
Bounded set      86 161
Branch      225
Brouwer — Kleene ordering      85
Cantor set      185
Cantor — Bernstein theorem      66
Cantor's theorem      96
Cantor, Georg      1 90 99 101
cardinal number      68 130 140
Cardinality      65 68
Cartesian product      21 57
Cauchy sequence      181
Chain      34
Characteristic function      91
Choice function      138
Closed interval      179
Closed set      182
Closed unbounded filter      208 212
Closed unbounded set      208 212
Closed under operation      55
Closure      60
Closure point      145 212
Coanalytic set      278
Cofinal sequence      143
Cofinality      163
Cofinite set      202
Cohen, Paul      101 139 269 275—277
Collection      9
Commutativity      13 94
Comparable      34
Compatible      26 237
Complete linear ordering      87
Completion      87
Complex number      179
composition      21
Computation      48 115
Concatenation      62
Condensation point      190
Condition      275
Connectives      5
Constant      7 57
Constructible model      271
Constructible set      273
Continuous function      145 182
Continuum      92
Continuum Hypothesis      101 141 268
Convergence      145
Coordinate      57
Countable additivity      150
Countable set      74
Counting measure      153 204
Cumulative hierarchy      257
Cut      88
De Morgan laws      14
Decimal expansion      86
Decoration      261
Decreasing sequence      144
Dedekind cut      88
Dedekind finite set      97
Dense linear ordering      83
density      203
Derived set      191
Descriptive set theory      278
Determined      281
Diagonal intersection      210 212
Diagonalization      90
Difference      13
digit      174
Disjoint      14
Distributivity      14 94 122 160
Division      173 178
Domain      19
Double induction      46
Element      1
Empty sequence      46
Empty set      6 8
Equipotent      65
Equivalence class      30
Equivalence relation      29
Erdoes — Dushnik — Miller Theorem      222
Erdoes — Rado theorem      223
expansion      178
exponentiation      54
Exponentiation of cardinals      95
Exponentiation of ordinals      122
Extension      24
Extensional relation      254
Factorial      48
Fibonacci sequence      50
Filter      201
Finite additivity      204
Finite character      144
Finite intersection property      180 202
Finite sequence      46
Finite set      69 72
Fixed point      69
Forcing      275
Function      23
Function into      24
Function on      24
Function onto      24
GCH      165
Generic set      236

Godel, Kurt      3 101 269 271 274 279 282 283
Goodstein sequence      125 126
Graph      261
Greatest element      35
Greatest lower bound      35
Hahn — Banach theorem      148
Hahn, Hans      149
Hamel basis      146
Harrington, Leo      281
Hartogs number      130
Hausdorff's Formula      168
Hereditarily finite      114
Hilbert, David      101
Homogeneous set      217
Ideal      202
Identity      4
Image      20
Inaccessible cardinal      162 168
inclusion      12
Incomparable      34
Incompatible      237
Increasing function      105
Increasing sequence      160 181
Induction principle      42 44 114 260
Inductive set      40
Infimum      35
Infinitary operation      198
Infinite product of cardinals      157
Infinite sequence      46
Infinite set      69
Infinite sum of cardinals      155
Initial ordinal      129
Initial segment      104
Injective function      25
INTEGER      171
Integer part      174
Intersection      7 13 14
Inverse      20
Inverse image      20
Invertible function      25
Isolated point      184
Isomorphic structures      59
Isomorphism      36 58
Isomorphism type      260
Jensen's Principle      234
Jensen, Ronald      274
k-complete filter      246
Koenig's lemma      227
Koenig's Theorem      158
Least element      35
Least upper bound      35
Lebesgue measure      152
Length      62
Lexicographic ordering      82
LIMIT      160 181
Limit cardinal      162
Limit point      212
Linear functional      148
Linear ordering      34
Linearly independent      146
Linearly ordered set      34
Lower bound      35
Mahlo cardinal      249
Mapping      23
Martin's Axiom      237 238
Martin, Donald Anthony      281 282
Maximal element      35
Measurable cardinal      247
Measure      150 204 241
Measure problem      241
Minimal element      35
Model      270
Monochromatic set      217
Monotone function      69
Mostowski's Lemma      255
Multiplication      54 172 177
Multiplication of cardinals      94
Multiplication of ordinals      121
n-ary operation      57
n-ary relation      57
n-tuple      56 118
Natural number      41
Node      225
Nondecreasing sequence      181
Normal form      124
Normal ultrafilter      249
One-to-one function      25
Open interval      179
Open set      182
Operation      7 55
Order type      79 113 260
Ordered field      178
Ordered n-tuple      56
Ordered pair      17
Ordered set      33
Ordering      33
Ordinal number      107
Palindrome      64
PARAMETER      5
Paris, Jeffrey      282
Partition      31
Peano arithmetic      54
Peano, Giuseppe      54
Perfect set      185
Power set      10
Prime ideal      205
Principal filter      201
Principal ideal      202
Principle of dependent choices      144
Product of an indexed system      26
Projection      62
Projective determinacy      282
Projective set      278
Proper subset      12
Property      1
Quantifiers      5
Ramsey's theorem      218 219
RANGE      19
Rank      255
Rational number      173
Real number      89
Recursion theorem      47 115 260
Reflexive relation      29
Regressive function      209 212
Regular cardinal      161
Relation      29
Restriction      24
Russell's paradox      3
Russell, Bertrand      2
SEQUENCE      46
Set      1
Set of all sets      2
Set of representatives      32 139
Set of sets      2
Silver's Theorem      212
Singleton      17
Singular cardinal      160
Skolem — Loewenheim Theorem      274
Solovay, Robert      152 280 281
Statement      6
Stationary set      209 212
Steel, John      282
Strategy      280
Strict ordering      33
Strong limit cardinal      168
Structure      56 58
Subsequence      181
Subset      6
Successor      40 51
Successor cardinal      162

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