Smullyan R.M., Fitting M. — Set theory and the continuum problem :: Электронная библиотека попечительского совета мехмата МГУ

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Smullyan R.M., Fitting M. — Set theory and the continuum problem

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Название: Set theory and the continuum problem

Авторы: Smullyan R.M., Fitting M.

Аннотация:

A lucid, elegant, and complete survey of set theory, this volume is drawn from the authors' substantial teaching experience. The first of three parts focuses on axiomatic set theory. The second part explores the consistency of the continuum hypothesis, and the final section examines forcing and independence results.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 289

Добавлена в каталог: 31.10.2010

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

Предметный указатель

Extensionality      116
Extraordinary      11
Field      43
Filter      262
Fine structure      271
finite      4 39 99
Finite character      56
Finite support      255
First-order definable      see definable first-order
First-order property      14
First-order swelled      see swelled first-order
First-order universe      153
First-order universe, well founded      153
First-order Zermelo universe      see Zermelo universe first
First-order Zermelo-Fraenkel universe      see Zermelo — Fraenkel universe first-
Fixed point      36
Fixed point lemma      98
Forces      192 196
Forces, weakly      197
Forcing      189
Forcing condition      203 229 236 254
Formula      128
Formula, $\Delta_{zero}$       145
Formula, $\Sigma_{zero}$       145
Formula, A      129
Formula, atomic      128
Formula, pure      129
Formula, with constants      129 191
Frame      191
Frame, augmented      191
Free occurrence      128
Frege set theory      10
Function      23
Fundamental theorem of cardinal arithmetic      102 104
G $\ddot{o}$ del’s isomorphism theorem      179
Generalized induction      see induction generalized
Generalized transfinite recursion      see transfinite recursion generalized
GENERIC      262
GREATEST      35 44
Hartog’s function      102
Hartog’s theorem      101
Henkin closure condition      132
Henkin-closed      132
Henkin-closure      133
Hereditary cardinality      178
Identity function      70
IFF      16
Immediate extension      58
Immediately in      204
Incompatible      230 263
Individual      166
Induction      27
Induction, complete      32
Induction, double      32
Induction, generalized      117
Inductive      30
Inductive, minimally      33
Inductive, under       see $g$

-inductive
Infinite      3 4 39
Initial element      88 116
Inner model      189
Intersection      20
INTO      24
Intuitionistic logic      196
Inverse      70
Isomorphism      71 117
Iterated forcing      274
Knaster — Tarski theorem      98
Kripke semantics      191
L $\ddot{o}$ wenheim’s theorem      130
Larger      96
Law of additive absorption      103
Law of multiplicative absorption      104
LEAST      35 44
Levy’s basis theorem      177 178
Limit cardinal      181
Limit element      45
Limit ordinal      65
Lindenbaum construction      60
Linear ordering      44
Lower section      47 71
Lower section, proper      47
M.S.T.V.      137
MAP      24
Mathematical induction      see induction
Maximal      55
Maximal principles      55
Maximal principles, Hausdorff      58
Maximal principles, Kuratowski      56
Maximal principles, Tukey — Teichm $\ddot{u}$ ller      56
Minimally superinductive      see superinductive minimally
Modal logic      191
Modal model      191
Model of       185
Model of       184
Model, modal      see modal model
modus ponens      201
Monadic      168
Monotone      98
Monotone, increasing      137
Montague — Levy reflection theorem      137 138
Morse — Kelley set theory      13
Mostowski — Shepherdson mapping      115 121 123
Mostowski — Shepherdson mapping, theorem      122
Mostowski — Shepherdson — Tarski — Vaught theorem      137
Moves backwards      72
Natural number      3 64
Necessitation rule      193
Nest      34
Non-classical logic      189
Non-denumerable      4 39 99
Non-trivial      236
Normalizes      244
Number, cardinal      see cardinal number
Number, natural      27 30;
Number, ordinal      see ordinal number
Onto      24
Operation      23
Order      142
Ordered pair      19
Ordinal hierarchy      82
Ordinal number      64
Ordinal number, Robinson’s definition      94
Ordinal sequence      75
Ordinary      11 15
Over A      129
Partial ordering      43 195

Peano postulates      27
Permutation      255
Permutation group      243
Platonist      10
Possible world      203
Possible world semantics      191
Power      8
Power set      7
Predecessor      45
Preordering      195
Principle E      59
Progressing      34
Progressing, slowly      41 52
Progressing, strictly      50
Proper subset      see subset proper
Proper well ordering      see well ordering proper
Pseudo-constructible      179
Pseudo-construction      179
Ramified      273
RANGE      23
Rank      81
Realist, mathematical      10
Reflection principles      128
Reflects      131
Reflects, completely      131
Reflects, with respect to $\varphi$       131
Reflexive      43
Reflexivity axiom      196
Regular      207
Relation      23
Relation, single-valued      23
Relational structure      194
Relational system      115
Relational system, proper      115
Relativization      182
Relevant      158
Replacement Theorem      193
Restriction      44
Reverse diagonal      254
S4 model      202
S4 model      195
S4 regular model      207
s5      195
Sandwich principle      35 50
Satisfiable      130
Schr $\ddot{o}$ der — Bemstein theorem      8
Separation      14
Separation principle      12
SEQUENCE      40
Set      14
Sierpi $\acute{n}$ ski’s theorem      109 112
Similar      96
Singleton      18
SIZE      96
Skolem — L $\ddot{o}$ wenheim theorem      131
Slowly progressing      see progressing slowly
Smaller      7 96
Special      60 255
Ssentence, entence      168
Stabilize      223
Stable      163
Standard model      184 259
Standard model, countable      260
Strictly progressing      see progressing strictly
subclass      14
Subformula      128
Subgroup      245
Subset, proper      7
Substitution      129 169
Substitution, function      169
Successor      45
Successor ordinal      65
Supercomplete      16
Superinduction, double      49
Superinduction, proof by      48
Superinductive      48
Superinductive, minimally      48
Swelled      16 153
Swelled, first-order      153
Tarski — Vaught theorem      131 132
Tarski — Vaught theorem, class version      134
Theorem G      177
Theorem GI      179
Theorem K      179
Transfinite induction      46
Transfinite recursion      74 77
Transfinite recursion, generalized      121
Transitive      16 43
Transitive closure      177
Transitivity axiom      196
Trichotomy      101
Trichotomy principle      38
True at       192
True at a world      192
True over A      131
Truth      170
Truth in relational systems      130
Truth Lemma      268
TYPE      56 167
Uncountable      4 99
UNIVERSAL class      14
Universal generalization      201
Unordered pair      11 19
Unramified      273
Urelements      243
Valid      192
Valuation      170
Valuation function      170
Variable      128
Von Neumann’s principle      91 92
Weakly forces      see forces weakly
Well founded      88 93 116
Well ordered      35
Well ordering      44
Well Ordering Principle      38
Well ordering theorem, Zermelo      54
Well ordering, fundamental theorem of      72
Well ordering, proper      71
Well ordering, slow      52
Zermelo set theory      12
Zermelo universe      26 30
Zermelo universe, first-order      181
Zermelo — Fraenkel      see $ZF$

Zermelo — Fraenkel set theory      12 154
Zermelo — Fraenkel universe      73
Zermelo — Fraenkel universe, first-order      153
Zermelo — Fraenkel universe, first-order, well founded      153
Zorn’s Lemma      57

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