Tourlakis G.J. — Lectures in Logic and Set Theory: Set Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Tourlakis G.J. — Lectures in Logic and Set Theory: Set Theory

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Название: Lectures in Logic and Set Theory: Set Theory

Автор: Tourlakis G.J.

Аннотация:

Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2003

Количество страниц: 575

Добавлена в каталог: 29.11.2009

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Предметный указатель

"Real sets"      110
$\Delta$ -system      555
$\Delta$ -system, root of      555
$\Delta_{0}$ -formulas      380
$\epsilon$ -least      244
$\epsilon$ -minimal element      239
$\epsilon$ -minimum      244
$\epsilon$ -smallest      244
$\exists$ -introduction      37
$\forall$ -introduction      44
$\gamma$ -closed      437
$\Gamma$ -induction      438
$\Gamma$ -proof      38
$\Gamma$ -theorem      37
$\kappa$ -antichain condition      553
$\kappa$ -chain condition      553
$\lambda$ -notation      202
$\mathfrak{M}$ -formula      55
$\mathfrak{M}$ -instance      56
$\mathfrak{M}$ -term      55
$\mathscr{R}$ -closed      21
$\subseteq$       21
$\tau$ -term      76
$\varepsilon$ -numbers      426
$\varepsilon$ -term      76
1-1 correspondence      64 204 273
1-1 function      see "Function"
Absolute formula      382
Absolute term      382
Absolutely provable      38
Absoluteness of rank      394
AC      215 274
AC, global      226
AC, strong      226
Aczel, P.      498
Addition      246
Addition over $\omega$       246
Addition over $\omega$ is associative      248
Addition over $\omega$ is commutative      247
Adjacency map      269
Adjacency matrix      269
Alephs      465
Algebraic topology      275
Algorithm      283
Alphabet      7 13
Ambiguity      25
Ambiguous      25 498
Antichain      520
Antinomies      104
Apostol, T.      228
Argot      40
Arithmetization      90
Arity      9
Array      233
Ascending sequence      348
Associativity      17 256
At most enumerable      442
atom      see "Urelement"
Axiom      8
Axiom of (unordered) pair      145 211
Axiom of Choice      see "AC"
Axiom of collection      163 204
Axiom of constructibility      408
Axiom of Dependent Choices      298
Axiom of foundation      158
Axiom of infinity      234
Axiom of Power Set      180
Axiom of replacement      161 163 371
Axiom of union      151
Axiom, comprehension      121
Axiom, logical      8
Axiom, nonlogical      8 37
Axiom, nonlogical of regularity      159
Axiom, nonlogical, urelements are atomic      116
Axiom, special      8
Axiomatic theories      39
Axiomatized      39
Axioms, logical      35
Barwise, J.      192 368 395
BASIC language      108
Bemays, P.      34 42 315
Berry's paradox      104
Beth      516
Bijection      see "1-1 correspondence"
Binary digit      455
Binary notation      455
Binary relation      see "Relation"
Bit      455
Blum's speedup theorem      228
Blum, E.      228
BNF      18
Boolean      9
Boolean addition      270
Boolean sum      271
Bound variable      19
Bourbaki, N.      5 43 229
Brouwer, L.E.J.      4 12
Burali-Forti, C.      122
c.c.c.      553
Calculational proof      85
Cantor, G.      105 122
Cardinal      207 458 467
Cardinal multiplication      472
cardinal number      431 458 467
Cardinal product      472
Cardinal successor      465
Cardinal, inaccessible      483
Cardinal, strongly inaccessible      483
Cardinal, weakly inaccessible      483
Cardinality      431 458 467
Cardinals, product of family      485
Cardinals, sum of      470
Cardinals, sum of family      484
Cartesian product      189
Cartesian product of many classes      192
Category theory      275
ch      466
Chain      354 520
Choice function      216
class      136
Class term      134
Class, $\epsilon$ -closed      237
Class, domain of      195
Class, f-closed      434
Class, proper      137
Class, R-closed      495
Class, range of      195
Class, transitive      236
Closed formula      20
Closed term      20
Closed under      21 434
Closure      21 see
Cofinal subsets      478
Cofinality      478
Cohen Extension      524 526
Cohen generic real      553
Cohen, P.J.      229 467 487 526
Collapsing Cardinals      551
Collapsing function      310
Collection      149
Collection axiom      see "Axiom"
Commutative diagram      275
Compactness Theorem      65
Comparable      520
Compatible      520
Complement      145
complete      97
Complete arithmetic      40
Complete lattice      349
Completeness      6

Completeness theorem      54 64 65 97
Completion      97
composition      195 see
Computer programming      232
Concatenation      13 252
conditions      520
Congruence      261
Conjunction      17
Conjunctionally      85
Connectives      9
Conservative      68 74
Conservative extension      72 168
Consistency      61 531
Consistency theorem      64 65
Constant      10
Constant, imported      55
Constructible object      397
Constructible sets      396
Constructible universe      219 229 284 395
Construction formative      43
Continuum Hypothesis      3 466
Correct      88
Correct theory      88
Countable      64 90 314 442
Countable chain condition      553
Course-of-values induction      281 294
CTM      314
Cumulative hierarchy      359
De Morgan's laws for classes      154
De Morgan's laws, generalized      212
Decision problem      41
Dedekind finite      449
Dedekind infinite      449
Dedekind, R.      449
DEDUCE      38
Deduction Theorem      49
Deductions      1
Definability      61 62
Definability in a structure      61
Definition by recursion      26
Dense      520
Dense below      559
Denumerable      442
Derivation      22
Derived rule      37 39 41
Devlin, K.J.      229
Diagonalization      121 156
Difference      250
Difference of two classes      141
Difference over $\omega$       250
Disjoint classes      141
Disjoint union      412
Distributive laws      95 212
Distributive laws for $\omega$       282
Distributive laws for $\times$       213
Distributive laws, generalized      212
Domain      54
Double induction      248 300
Dummy renaming      46
Elimination of defined symbols      69 71
Embedding      318
Empty set      100 111 131
Entscheidungsproblem      41
Enumerable      442
Equinumerous      431
Equipotent      431
Equivalence class      276 277
Equivalence relation      276
Equivalence theorem      52
Existential formula      67
Explicit listing      147
Expression      2 8 13
Extension      7 194
Extension of a condition      520
Extension, Cohen      524
Extension, generic      524
Extensional      31 312
Extensionality      67
Family of sets      150
Family, indexed      206
Family, intersection of      153
Family, quasi-disjoint      555
Family, union of      150
Feferman, S.      228 447 530
Filter      521
Filter, generated by a chain      522
Finitary      4
Finitary rule      503
finite      389
Finite sequence      251
Finite sequence, length of      251
Finitely satisfiable      98
First incompleteness theorem      87
First order definable      111
Fixed point      351 438
fixpoint      351 438
Forcing      315
Forcing conditions      520
Forcing language      528
Formal Interpretation      78
Formal interpretation of a theory      83
Formal isomorphism      84
Formal language      111 115
Formal language, first order      7
Formal model of a theory      83
Formal natural numbers      see "Set"
Formalize      6
Formalized      3
Formula form      35
Formula schema      35
Formula, absolute      382
Formula, mixed-mode      62
Formula, prime      29
Formula, propositional      29
Formula, satisfiable      31
Formula, tautology      31
Formula, unsatisfiable      31
Foundation axiom      102
Fraenkel, A.A.      105
Free for      33
Free variable      19
Frege, G.      121
Function      199
Function diagram      275
Function substitution      201
Function, bijective      204
Function, collapsing      310
Function, continuous      348
Function, countably continuous      348
Function, diagram      275
Function, diagram, commutative      275
Function, expansive      353
Function, inclusive      353
Function, increasing      348
Function, injective      203
Function, inverse of      273
Function, left inverse of      272
Function, left-invertible      274
Function, monotone      348
Function, non-decreasing      348
Function, one-to-one      203
Function, order-preserving      317
Function, partial      199
Function, right inverse of      272
Function, right-invertible      274
Function, surjective      204
G-interpretation      525
GCH      466 484
Generalization      45 120
Generalized Continuum Hypothesis      408 466 484

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