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Marcja A., Toffalori C. — A Guide to Classical and Modern Model Theory
Marcja A., Toffalori C. — A Guide to Classical and Modern Model Theory

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Название: A Guide to Classical and Modern Model Theory

Авторы: Marcja A., Toffalori C.

Аннотация:

Written for graduate students and mathematicians not familiar with logic, this book explains the fundamental tenets of model theory and emphasizes their frequent connections to algebra and geometry. Marcja (University of Florence) and Toffalori (University of Camerino) examine quantifier elimination, model completeness, imaginary elements, Morley's theorem on uncountable categoricity, the classification problem, and o-minimality.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 369

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adiacency relation      280
Algebraic geometry      291
Algebraic numbers, complex      87
Algebraic numbers, real      87
Algebraically independent set      170
Algorithm      39 80
Amalgamation      231 234
Analysis, complex      345
Annihilator      42
Artin’s conjecture      86 96—103
Artin’s theorem      95
Atlas      299
Atomic set      198
Automorphism      5
Ax — Kochen — Ershov theorem      100
Ax’s theorem      60
Back-and-forth property      10
Basis      169
Baur — Monk theorem      70 74
Biinterpretability      279—286 288 290 339
Boolean space      136 180
Boundary point      322
Cantor — Bendixson rank      155 159
Cantor’s theorem      12
cell      320
Cell decomposition theorem      324 329
Character, finite      228 233
Character, local      228 233
Cherlin’s conjecture      303 310
Chevalley’s theorem      59
Church — Turing thesis      39 80
Class classification problem      20 221—227 289
Class elementary      22 105 221
Class of fields      25 103
Class of finite sets      22
Class of graphs      280
Class of infinite sets      22
Class of modules      27
Class of nilpotent groups of class      2 281
Class of ordered fields      26
Closure, algebraic      133 172 287 328
Closure, definable      133 172
Closure, differential      209
Closure, real      175
Coheir      238 252 290
Compactness      18
Compactness, theorem of      18 243 325 327
COMPLEX      37
Connected component      189
Construction      199
Constructive set      38 58 118 134 198 199 220 271 292 295
Coordinate chart      299
Cylindrical algebraic decomposition      80
Definable manifold      340
Definable sets      35—42 45 59 78 112 121 126 129 133—136 222 280 320 344 345
Definable sets, Boolean algebra of      36 134 143 219
Definable sets, convex      346
Definable sets, definably connected      322
Definable sets, indecomposable      190
Dependence      227
Dependence relation      180 184 328
Dependence relation, algebraic      170
Dependence relation, linear      169
Derivation      109 307
Descriptive set theory      222 289
Difference degree      289
Differential algebra      209
Differential degree      287
Differentially algebraic      210
Differentially transcendental      210
DIMENSION      294—297
Dimension of a definable set      328
Dimension of a tuple      328
Dimension of a vectorspace      169
Dimension theory      327
Effective procedure      40 44 79
Ehrenfeucht — Mostowski model      274 290
Elementary Chain Theorem      18 144
Elementary equivalence      324 347
Elimination of imaginaries      125 194 307
Elimination of imaginaries, uniform      125 300
Elimination of quantifiers for      52
Elimination sets      43
Embedding      4 9—18 85 88 103
Embedding, elementary      13 85 103
Embedding, existential      14 89 105
Endomorphism      5
Existence property      270
Exponential set      342
Extension      5 228 234
Extension, elementary      14
Extension, non forking      237 238 240
Field of definition      194
Field, $\omega$-stable      220
Field, algebraic closure of      33 86 93 103 117
Field, algebraically closed      26 32 45 80—82 86 103 105 117 134 160 184 230 239 255 284 287 291 294
Field, complex, elimination of quantifiers for      82
Field, constant Subfield of      110 116
Field, difference      115
Field, difference, existentially closed      117
Field, difference, inversive      116
Field, differential      109 209
Field, differential closure of      111 115
Field, differential, existentially closed      110 115 209
Field, Differentially Closed      106 109—115 119 134 211 220 239 242 290 291 304 307
Field, differentially closed, axioms for      111
Field, elimination of imaginaries for      126
Field, existentially closed      239 290 307
Field, existentially closed with an automorphism      291
Field, fixed Subfield of      116
Field, formally real      95
Field, Henselian      99
Field, imperfection degree of      114
Field, locally compact      98
Field, locally compact of complex numbers      33
Field, locally compact of meromorphic functions      110
Field, locally compact of rational functions      109
Field, model completeness of      91
Field, of p-adic numbers      102
Field, ordered      129 316 327
Field, ordered, o-minimal      317
Field, ordered, real closure of      180
Field, p-adic      86
Field, perfect      113
Field, Pseudofinite      26 102 118 288 290
Field, quantifier elimination for      54— 61
Field, real      321
Field, real closed      43 78—82 87 95 104 105 129 134 239 313 317
Field, real closed, elimination of imaginaries of      129—131
Field, real closed, model completeness of      93
Field, real closed, quantifier elimination for      61—68
Field, real closed, theory of      27
Field, real, elimination of quantifiers for      82
Field, residue      101 102
Field, separably closed      112—115 119 239 242 290 307
Field, structure of      3
Field, superstable      220
Field, transcendence basis of      33
Field, transcendence degree of      33 86 184
Field, Valued      99 100 102
Field, with an automorphism      117
Finite in uniformly      330
Fischer — Rabin theorem      80
forking      233 237 287
Formal Laurent series      98
Formula      5
Formula, atomic      6
Formula, existential      8 88
Formula, finite      330
Formula, normal form of      8
Formula, positive primitive      41
Formula, quantifier free      8
Formula, T-equivalent      43
Formula, true in a structure      5 7
Formula, universal      8 88
Fra$\"{\i}$sse’s theorem      13
Frobenius morphism      113 116 118 174
Function field      306
Function, definable      297—299
Function, elementary      16 135 196
Generic element      190
Geometry      286
Goedel Incompleteness Theorem      40 280
Graph      280
Graph, random      231
Graph, structure of      3
Group, $\omega$-stable      184—192 220 302 303 310
Group, abelian-by-finite      284
Group, algebraic      301—304
Group, centre of      121
Group, definable      302 317
Group, existentially closed      106 119
Group, linear      121 301
Group, linear algebraic      302
Group, o-minimal      315
Group, of finite Morley rank      303 310
Group, of finite type      305
Group, ordered abelian      101
Group, ordered abelian, divisible      313
Group, pp-definable      283
Group, quotient      122
Group, special      122
Group, structure of      3
Group, torsionfree abelian      222 289
Groups, elementary class of      105
Heir      238 252 290
Hensel’s Lemma      98
Herbrand universe      19
Hilbert’s basis theorem      38 292
Hilbert’s Nullstellensatz      82 86 93 119 292
Hilbert’s Seventeenth Problem      86 95 119
Homomorphism      4
Homomorphism, pure      151
Hrushovski — Weil theorem      303 310 340
Ideal element      139
Ideal, differential      210
Ideal, differential, prime      210
Ideal, prime      293
Ideal, radical      292
Independence      287
Independence system      236
Independence system, good      231 249
Independent set      177
Induction principle      7 29
Infinite sets theory of      22
Injectivity-implies-surjectivity theorem      60
Interpretability      279
Invariance      228 233
Invariant statement      70 73
Invariant system      225
Irreducible components      293
Isomorphism      5
Isomorphism, partial      10
Knight - Pillay - Steinhorn theorem      78
Kolchin constructible      112 134
Kolchin topology      112
Lagrange’s Theorem      43 280
Language      1
Lindstroem’s theorem      7 29
Linear order, class of      23
Linear order, dense      52—54 93
Linear order, dense without endpoints      24 32
Linear order, discrete      24 47—52 93
Linear order, elimination of quantifiers for      48
Linear order, expansion of      313
Linear order, theory of      23 218
Linear orders      78
Linearly independent set      169
Locally modular      288
Loewenheim — Skolem theorem      28 85 182 226 274 275
Loewenheim — Skolem theorem, downward      19 29
Macintyre’s theorem      192 284
Manifold      299—302
Manifold, affine      299
Manifold, semiaffine      299
Manin — Mumford conjecture      305 310
Model      8
Model companion      111 115 117 215
Model, $\lambda$-saturated      144
Model, $\lambda$-universal      145
Model, homogeneous      147
Model, minimal      87
Model, prime      87 133 196—209 216 220 254 270 328
Model, saturated      133 143—150 180
Model, weakly $\lambda$-homogeneous      145
Module      239
Module, algebraically compact      152
Module, indecomposable      153
Module, pure injective      152
Module, pure injective hull of      152
Modules      27 41 290
Modules, theory of      68—76
Monotonicity theorem      348
Mordell — Lang Conjecture      304—310
Mordell’s conjecture      304
Morley degree      161 189 220 241
Morley degree of a type      165
Morley rank      158—168 180 220 230 241 288 294 298 307 313 346
Morley rank of a type      165
Morley’s existence theorem      271
Morley’s theorem      133 181 271 273— 279 290
Morphism      297 302
n-type      293
N-type, complete      137
Neumann’s lemma      70 72
Nilradical      108
Non-forking extension      252 259
Number field      304
Omitting types theorem      157 198 217
Open box      322
Open mapping theorem      259 273
Order property      237 243
Ordered field      104 313
Ordered field of reals      65 95
Ordered field, real closure of      93
Ordered field, structure of      3
Orthogonality      255
p-adic topology      96
p-basis      114
P=NP problem      80
Parameters      35
Partition      330
Polish space      222
Polynomial      110
Polynomial, difference      116
Polynomial, differential      110 115
Polynomial, separable      113
Pp-elimination of quantifiers      70—76
Pp-formula      41 69 151
Pp-type      152
Predecessor      47 263
Presentation      264
Priifer group      155
Projective space      299
Pure injectivity      150
Quantifier elimination      43—82 87 88 345
Random graph, theory of      239
Rank      158
REAL      38 341
Real analysis      341
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