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| Marcja A., Toffalori C. — A Guide to Classical and Modern Model Theory |
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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,  -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 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, -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,  -saturated 144
Model, -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 -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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