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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
$\alpha$-categorical      2 482 507
$\alpha$-complete filter      227
$\alpha$-enlargement      283
$\alpha$-good ultrafilter      386
$\alpha$-homogeneous model      297
$\alpha$-isomorphism property      305
$\alpha$-like model      557
$\alpha$-omit      87
$\alpha$-realize      87
$\alpha$-regular filter      248
$\alpha$-saturated model      256 283 292
$\alpha$-saturated over V(X)      283
$\alpha$-standard model      529
$\alpha$-universal model      255 297
$\alpha$-universal with respect to K      297
$\Delta_{0}$ formula      110
$\omega$-categorical theory      104
$\omega$-complete      82
$\omega$-consistent      81
$\omega$-homogeneous      113
$\Omega$-logic      82
$\omega$-model      81 515
$\omega$-rule      82
$\omega$-saturated      100
$\omega$-Vaught Test      139
$\Sigma_{1}$-formula      110
Abelian group      40
Absolute formula      562
Absorption laws      38
Abstract logic      128
Additive function      386
Additive number theory      43
Admit a pair of cardinals      154
Admit a pair of cardinals omitting a type      532
Admit a triple of cardinals      532
Admit elimination of quantifiers      202
Algebraic in a theory      496 529
Algebraically closed field      41
Algebraically independent      348
Algebraically prime model      195
Amalgamate      196
Amalgamation property      195
antisymmetric      580
Antisymmetric property      37
Archimedean ordered field      70
Arithmetical predicate      415
Arithmetical set      125
Arithmetical statement      415
Arithmetically saturated model      125
Aronsajn tree      525
Arrangement      51 55
Artin’s conjecture      368
ASSIGNMENT      7
Associativity      39
Atom of Boolean algebra      39
Atomic Boolean algebra      39
Atomic element of a Boolean algebra      373
Atomic formula      22
Atomic model      97
Atomic theory      97
Atomless Boolean algebra      39
Atomless element of a Boolean algebra      373
Automorphism theorem      172
Automorphism type      176
Autonomous set of formulas      426
Axiom of Choice      584 593
Axiom of constructibility      238
Axiom of regularity      588
Axioms of a theory      12 37
Back and forth condition      114
Back and Forth Construction      98
Back and Forth Lemma      298
Base set      263
Basic elementary class      220
Basic formula      50
Basic Horn formula      407
Bernays set theory      594
Bernays — Morse set theory      595
Beth’s Theorem      90
Bit of a tuple in a Boolean algebra      379
Boolean algebra      38
Boolean combination      50
Bound variable      22
Bounded elementary chain theorem      287
Bounded elementary embedding      266
Bounded elementary submodel      266
Bounded limit ultrapower      457
Bounded quantifier      265
Bounded quantifier formula      265 562
Bounded ultrapower      269
Branch of a tree      244
Built up from constants      66
Built-in Skolem functions      165
Cantor diagonal method      592
Cardinal      586
Cardinal exponent      586
Cardinal of a language      19
Cardinal of a model      21
Cardinal power      586
Cardinality of a set      586
Cartesian product      579 580
Categorical in power $\alpha$      2 482 507
Cauchy sequence      351
ch      586
Chain      580
Chain of Models      140
Chain, elementary      140
Chang — Makkai Theorem      333
Chang's Two Cardinal Theorem      520
Chang’s Conjecture      156 534
Characteristic of a field      41
Choice axiom      593
Church’s thesis      110
Classification theory      502
Closed set of ordinals      246
Closed theory      12 36
Closed unbounded set      246
Closed under directed unions      146
Closed under elementary equivalence      220
Closed under reduced roots      446
Closed under roots      354
Closed under ultraproducts      220
Closed under union of well ordered chains      146
Closure property      128
Cofinal      589
Cofinality      589
Collection scheme      593
Commutative ring      40
Compact class of models      446
Compactness Theorem      11 33
Companion Operator      205
Completable formula      97
Complete arithmetic      42
Complete embedding      448
Complete extension      448
Complete Formula      97
Complete number theory      42
Complete theory      17 37
Complete, $\alpha$-(filter)      227
Complete, $\omega$-(theory)      82
Completeness theorem      8 32
Completeness Theorem (Extended)      11 33
Completeness Theorem for $\omega$-logic      82
Completion of a model      448
Completion, valued field      351
Comprehension scheme      595
Comprehensiveness Theorem      284
Concatenation      584
Concurrent relation      290
Condition, forcing      209
Conditional sentence      14
Congruence relation      64
Connected partial ordering      580
Consequence      11 17 32 50
Consistent      9 25
Consistent with T      79
Constant      20
Constant symbol      18
Constructibility, Axiom of      238
Constructible set      559
Constructible universe      559
Continuum Hypothesis      586
Core Model      253
Corresponding relation      20
Cotheory      192
Countably compact logic      130
Countably homogeneous model      113
Countably incomplete filter      226
Countably prime model      99
Countably saturated model      100
Countably universal model      103
Cover of a model      404
Craig Interpolation Theorem      87
Craig lnterpolant      87
Cross section axiom      351
De Morgan laws      38
Deducible      9 25
Deduction      9
Deduction Theorem      10 25
Definable element      35 185
Definable function      461
Definable subset      259 559
Define explicitly      90 329
Define implicitly      90
Definitional extension      185
Degree of a field extension      348
Degree of a formula      496 497
Dense order      38
Descendingly a-complete ultrafilier      258
Detachment, rule of      9
Determined formula      421
Diagonal intersection      246
Diagram      68
Direct factor      321
Direct limit      322
Direct product      224 321
Direct product of formulas      428
Direct system      322
Directed relation      146
Discrete simple ordering      182
Distributive laws      38 40
Divisible torsion-free Abelian group      40
Downward Lowenheim-Skolem-Tarski Theorem      66
Effective process      423
Elementarily equivalent      32
Elementarily equivalent, abstract      129
Elementary chain      140
Elementary Chain Theorem      140
Elementary class      199 220
Elementary diagram      137
Elementary embedding      84
Elementary Embedding Theorem      172
Elementary extension      84 136
Elementary submodel      84 136
Elimination of quantifiers      50 202
End extension      85 163
Enlargement      283
Enumeration      584
Enumeration Principle      585
Equivalence relation      59 580
Equivalent      17
Equivalent formulas      50
Equivalent logics      129
Equivalent over Y      174
Erdos cardinal      555
Erdos notation      554
Erdos — Rado Theorem      510
Ershov’s Theorem      440
Essentially existential      125 322
Essentially finite direct power      431
Existence of nonstandard universes      268
Existence Theorem for Countably Saturated Models      102
Existence Theorem for Recursively Saturated Models      112
Existence Theorem for Special Models      296
Existential sentence      34
Existential-positive formula      319
Existentially closed      192
Expansion of a language      19
Expansion of a model      20
Expansion property      128
Expansion theorem      216 279
Extended Completeness Theorem      11 33
Extended Omitting Types Theorem      84
Extension of a model      22
Extension of a theory      37
External set      276
False in a model      7 32
Field      41
Field of characteristic zero      41
Field of prime characteristic      41
Field of sets      39
Filter      46 211
Filter generated by E      212
Finite cover property      404
Finite direct power sentence      412
Finite direct product      406
Finite direct product of formulas      428
Finite forcing companion      210
Finite forcing relation      209
Finite intersection property      46 166 212
Finite Iteration Theorem      463
Finite ordinal      582
Finite spectrum problem      597
Finitely axiomatizable      12 37
Finitely Generated Model      73
Finitely generic model      210
Finitely generic set      209
Finitely satisfiable      11
First-order predicate language      18
First-order theory      34
forking      505
Formal power series      352
Formula      22
Frayne’s Theorem      256
Frechet filter      211
Free variable      22
Fully compact logic      129
Function      20 579
Function symbol      18
Fundamental theorem of ultraproducts      217
Gap n conjecture      524
GCH      586
Generalized Continuum Hypothesis      586
Generalized m-logic      83
Generated from a set of indiscernibles      171
Germ of a meromorphic function      371
Goedel completeness theorem      33
Good Ultrafilter      257 386
Group      40
Hanf number      134
Hausdorff maximal principle      585
Hensel field      353
Henselization      354
Hensel’s Lemma      353
Hereditary set      340
Homogeneous model      113 297
Homomorphic      70
Homomorphic image      71
Homomorphically embedded      71
Homomorphism      71
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