Marcja A., Toffalori C. — A Guide to Classical and Modern Model Theory :: Электронная библиотека попечительского совета мехмата МГУ

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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.

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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

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Предметный указатель

Recursive sets      39
Recursively enumerable set      40
Residue field      99
Ressayre’s Uniqueness theorem      202 271
Ring, commutative      107
Ring, differential      109
Ring, existentially closed      106
Ring, ordered      317
Ring, reduced      109
Rings, elementary class of      105
Robinson’s Test      88—91
Rudin — Keisler relation      254 290
Ryll — Nardzewski’s theorem      217 220
SchanuePs Conjecture      343
Semialgebraic set      38 67 134
Semidefinite positive      95
Sentence      5 7
Separant      211
Shelah’s uniqueness theorem      220 270— 273 290
Sign change property      98
Small subset of Q      148
Smooth equivalence relation      223
Spectrum function      226
Stationarity over models      236
Stationary logic      290
Strong homogeneity theorem      147
Strongly minimal set      163 168—172 288 304
Structure, $R_{an, exp}$       345
Structure, $R_{an}$       5 344
Structure, $R_{exp}$       341
Structure, $\omega$ -stable      185 220 291 308
Structure, basis of      177
Structure, definable      40 121 302
Structure, dimension of      177
Structure, existentially closed      105 110 119
Structure, expansion of      5
Structure, extension of      85
Structure, interpret able      123
Structure, locally modular      283
Structure, minimal      77 168 176 179
Structure, o-minimal      78 178 179 313 318
Structure, restriction of      5
Structure, simple      232
Structure, stable      236
Structure, strongly minimal      168 256 282 287 292 308
Structure, superstable      241
Structure, trivial      283
Structure, two-sorted      100
Structure, universe of      2
Structure, unstable      236
Structure, X-definable      121
Structure, X-interpretable      123
structures      2
Structures, elementarily equivalent      10
Subanalytic set      344
Subanalytic set, globally      344
Subexponential set      342
Subgroup, definable, connected      188
Subgroup, pp-definable      41 69
Submodule, pure      151
Substructure      5 85
Substructure, elementary      14
Substructure, existential      15
Substructure, finitely generated      5
Substructure, generated      5
Successor      47 263
Symmetry      228 234
Tarski — Seidenberg theorem      38 67
Tarski — Vaught theorem      17 158
Tarski’s theorem      54 296 341
Terjanian’s counterexample      100 102
Terms      6
Theory      21 22
Theory of a class of models      21
Theory of a model      31
Theory of an equivalence relation      256
Theory of infinite sets      32 282
Theory of two equivalence relations      265
Theory of vectorspaces      34
Theory, $ACF_{0}$       33 57 87
Theory, $ACF_{p}$       26 32 33 45 57 77 88 149 169 184 197 219 261
Theory, $DCF_{0}$       111 112 197 209—217 287
Theory, $DCF_{p}$       115
Theory, $dLO^{+}$       48 50 51 77 87
Theory, $DLO^{-}$       24 32 52 53 160 174 181 182 217 218 226
Theory, $SCF_{p}$       114

Theory, $T_{p}$       102
Theory, $T_{\mathcal{R}}$       27
Theory, $\lambda$ -categorical      28
Theory, $\omega$ -stable      181—184 220 230 242 261 270 346
Theory, ${}_{\mathcal{R}}T$       68 70 73
Theory, ACF      26 45 54 58 88 91 111
Theory, ACF A      117 118 131 231 288
Theory, Booleanly A-categorical      219
Theory, categorical      133 274
Theory, classifiable      225 227 261—270
Theory, complete      19 30 102
Theory, completions of      31 45
Theory, consistent      21
Theory, decidable      40 44 342
Theory, deep      268
Theory, depth of      268
Theory, dLO      52
Theory, independence system of      228
Theory, kT      169
Theory, model companion of      105 117
Theory, model complete      34 46 85—96 102 103 117 119 212 288 342 344 345
Theory, not classifiable      237
Theory, o-minimal      78—79 178 226 234 313 344 345 348
Theory, presentable      264
Theory, RCF      27 33 61 65 66 80 87 88 91 93 95 104 111 129 175 197 341
Theory, rich      19
Theory, rosy      348
Theory, shallow      268
Theory, simple      227—235 249 289 290 328
Theory, stable      235—239 243
Theory, strongly minimal      76—77 163 168 182 184 220 221 225 227 236 239 261 274 346
Theory, superstable      239—242 252
Theory, totally transcendental      133 181 184 346
Theory, unstable      236 237
Theory, weakly o-minimal      346
Thorn-independence      348
Topological space, compact      140
Topological space, hausdorff      140
Topological space, totally disconnected      140
Transcendence basis      170 295
Transcendence degree      33 92 149 170 294
Transitivity      228 234
TREE      264
Tree, rank of      267
Tree, well founded      267
Trichotomy theorem      341
Turing machine      39 79 80
TYPE      133 136—143
type of      138
Type, algebraic      141 166
Type, complete      137
Type, consistent      137
Type, definable      238 244
Type, depth of      268
Type, generic      190 294
Type, isolated      141 156 198
Type, realization of      139
Type, regular      241
Type, RK-minimal      255
Type, stabilizer of      188
Type, stationary      240
Type, strongly regular      256
Ultrafilter      136
Uniqueness theorem      146
Universal domain      86
Universality Theorem      145
Valuation map      99 101
Valuation ring      99
Variety, abelian      304
Variety, algebraic      37 285 292 299
Variety, irreducible      293 294 298
Vaught’s conjecture      290 329
Vaught’s theorem      32
Vectorspace      230 239
Vectorspace, structure of      4
Vectorspace, theory of quantifier elimination for      75
Weak homogeneity theorem      145
Well ordered sets, class of      24
Word problem      107
Zariski geometries      285
Zariski structure      286
Zariski topology      38 117 292 296 297 302
Ziegler spectrum      154
Zilber’s conjecture      279—286 289 309 340
Zilber’s Indecomposability theorem      190 309
Zorn’s Lemma      94

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