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Chang C.C., Keisler H.J., Troelstra A.S. — Model Theory
Chang C.C., Keisler H.J., Troelstra A.S. — Model Theory



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Название: Model Theory

Авторы: Chang C.C., Keisler H.J., Troelstra A.S.

Аннотация:

Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory.
This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3 edition

Год издания: 1990

Количество страниц: 650

Добавлена в каталог: 02.07.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Horn formula      407
Huge cardinal      537
Hull, Skolem      171
Hypothesis of inaccessibility      590
Ideal in a Boolean algebra      373
Idealization Scheme      285
Idempotent laws      38
Identity axioms      25
Identity formula      24
Identity symbol      22
Implicitly define      90
Improper filter      211
Inaccessible cardinal      590
Incompletable formula      97
Inconsistent      9 25
Increasing sentence      13
Independent set of sentences      18
Independent unary relations      179
Indescribable cardinal      247
Indiscernible      169
Individual relative to V(X)      263
Induction scheme      42
Inductive order, theory of      382
Infimum of a set of ordinals      582
Infinite forcing companion      209
Infinite forcing relation      209
Infinite order in a group      78
Infinitely generic      209
Infinity axiom      592
Initial ordinal      586
Initial segment      583
Inner model      537
Inseparable theories      88 93
Integral domain      41
Internal definition principle      277
Internal formula      285
Internal Set      276
Internal Set Theory      285
Internalization Scheme      285
Interpolation theorem      17
Interpretation function      20
Invariants of a Boolean algebra      375
Inverse limit      322
Inverse system      322
Irreducible formula      496 498
Isomorphic chains      580
Isomorphic embedding      22
Isomorphic models      21
Isomorphism      21
Isomorphism of well orderings      583
Isomorphism property      128
Isomorphism Theorem for Ultrapowers      398
Isomorphism, partial      114
Iterated ultrapower      467 468
Joint embedding property      195
Jonsson algebra      554
Jonsson cardinal      538
Jonsson model      534
Keisler Sandwich Theorem      311
Keisler — Rabin Theorem      450
Kueker Finite Definability Theorem      330
Kueker's conjecture      506
Kurepa family      527
Kurepa Hypothesis      527
Kurepa Tree      259
Language      18
Limit cardinal      586
Limit ordinal      582
Limit ultrapower      451 452
Limited formula      265 562
Lindenbaum algebra      47 74
Lindenbaum’s Theorem      10 26
Lindstrom's Characterization      132
Lindstrom’s Second Theorem      135
Linear order      38
Local Ultrapower Theorem      281
Locally omit      80
Locally realize      79
Loewenheim number      129
Loewenheim — Skolem — Tarski Theorem      67
Logic, at      82
Logical symbols      22
Lyndon Interpolation Theorem      92
Mahlo number      246
Mahlo’s operation      247
main gap      507
Maximal consistent      9 25
Measurable cardinal      229
Medium compactness      245
Method of diagrams      68
Minimal nonstandard universe      291
Model companion      197
Model complete      186
Model completion      201
Model of a sentence      32
Model Pair      115
Model, first-order logic      20
Model, sentential logic      4 10
modus ponens      9 25
Monotonic function      386
Morley Categoricity Theorem      494
Morley Omitting Types Theorem      512
Morley rank      497 498
Mostowski collapse      272
Mostowski Collapsing Theorem      271
n-ary operation      580
n-ary relation      579
n-tuple      579
Narrowing a gap      254
Natural embedding      221
Natural model of set theory      45
Natural number      582
Neat elementary extension      156
Negation normal form (nnf)      93
Negative formula      313
Negative occurrence      92
Nonprincipal filter      166
Nonstandard analysis      70
Nonstandard element, Peano arithmetic      78
Nonstandard model of number theory      42
Nonstandard universe      266
Normal ultrafilter      239
Null set axiom      592
Number theory      42
O sharp      566
O sharp exists      566
Occur negatively      92
Occur positively      92
Occurrence Property      128
Omit a set of formulas      78
Omitting types theorem      80
Onto function      580
Open formula      51
Operation over X      580
Order of a group element      40
Order of a tree      244
Order type      583
Order type of a model of set theory      238
Ordered field      41
Ordered pair      579
Ordered tuple      579
Ordermorphic embedding      169
Ordermorphism      169
Ordinal      580
Ordinal sum      584
Outer extension      125 322
Overspill Principle      289
p-adic numbers      366
p-adic valuation      366
Pair, ordered      579
Pairs axiom      592
Partial isomorphism      114
Partial order, theory of      37
Partial ordering      580
Peano arithmetic      42
Pin down      134
Positive diagram      70
Positive occurrence      82
Positive sentence      13 72
Power of a language      19
Power of a model      21
Power of a set      586
Power set      588
Power set axiom      592
Preservation theorem      147
Preserved by reduced factors      419
Preserved under finite intersections      14
Preserved under homomorphisms      147
Preserved under intersections      15
Preserved under submodels      147
Preserved under unions of chains      147
Pressburger arithmetic      43
Prime model      99
Principal filter      46
Principal ideal in a Boolean algebra      374
Product of ultrafilters      463
proof      25
Proper filter      212
Pseudo-elementary Class      224
Quantifier axioms      24
Quantifier Property      128
Quotient Boolean algebra      374
r.e.      110
Ramsey cardinal      539
Ramsey’s theorem      168
Rank 1 valued field      371
Rank function      588
Rank of a set      588
Rank, Morley      497 498
Real closed field      41
Real closure      344
Realize a set of formulas      77
Realizing and Omitting Types Theorem      172
Recursive language      110
Recursive set      110
Recursively enumerable      110
Recursively Saturated Model      111
Reduced power      215
Reduced power sentence      412
Reduced product      215 216
Reduced product of formulas      428
Reduced product sentence      412
Reduct of a model      20
Reduction of a language      19
Reflexive property      37
Reflexive relation      580
Regular cardinal      589
Regular filter      248
Regularity axiom      592
Relation      20 579
Relation symbol      118
Relative algebraic closure      354
Relatively compact class of models      260
Relativization of a formula      125 321
Relativization Property      129
Relativization to V      594
Renaming Property      128
Replacement scheme      593 595
Representation theorem for Boolean algebras      39
Representation Theorem for Nonstandard Universes      457
Residue class field      352
Restricted Omitting Types Theorem      94
Restriction      580
Restriction of a closed theory      37
Rigid model      598
Ring      40
Robinson Consistency Theorem      91 119
Robinsonian analysis      262
Rowbottom cardinal      546
Rowbottom’s Theorem      545
Rule of Detachment      25
Rule of generalization      25
Rule of inference      25
Satisfaction relation, abstract      128
Satisfiable      10 16 32
Satisfy a formula      29
Satisfy a set of formulas      77
Saturated model      100 292
Saturated over V(X)      283
Saturated relative to A      511
Scott’s Theorem      238
Selective filter      481
Selective ultrafilter      262
Self-determining set of formulas      425
Semantically equivalent      17
Semantics      3
Semigroup      558
Sentence, first-order logic      24
Sentence, sentential logic      5
Sentenial axioms      24
SEQUENCE      584
Set relative to V(X)      263
Set-theoretic arithmetic      594
Silver’s Theorem      547
Simple expansion      19
Simple model      320
Simple order      38
Simple ordering      580
Singular cardinal      589
Skolem expansion      164
Skolem function      164
Skolem hull      165
Skolem normal form theorem      175
Skolem theory      164
Special Aronsajn tree      525
Special Horn sentence      419
Special model      295
Specializing chain      295
Spectrum problem      505
Stability theory      502
Stable in power a      485
Stable theory      485
Stand representation      172
Standard model of number theory      42
Standard set      276
Standardization Scheme      285
Star of A      267
Stretching Theorem      172
Strict basic Horn formula      418
Strict Horn formula      418
Strict well ordering      580
Strong homomorphism      321
Strong limit cardinal      586
Strongly compact cardinal      245
Subdirect product of models      419
Subformula      23
Submodel      21
Submodel complete theory      302
Submodel generated by X      34
Subset theorem      172
Subsets scheme      592
Substitution      22
Subtheory      37
Successor cardinal      586
Successor ordinal      582
Sum, ordinal      584
Supercompact cardinal      526
Superstable theory      505
Superstructure      263
Supremum of a set of ordinals      582
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