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Marker D. — Model theory: An introduction
Marker D. — Model theory: An introduction

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Название: Model theory: An introduction

Автор: Marker D.

Аннотация:

This book is a modern introduction to model theory which stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques, type spaces, prime models, saturated models, countable models, and indiscernibles and their applications. The author also includes an introduction to stability theory beginning with Morley's Categoricity Theorem and concentrating on omega-stable theories. One significant aspect of this text is the inclusion of chapters on important topics not covered in other introductory texts, such as omega-stable groups and the geometry of strongly minimal sets. The author then goes on to illustrate how these ingredients are used in Hrushovski's applications to diophantine geometry. David Marker is Professor of Mathematics at the University of Illinois at Chicago. His main area of research involves mathematical logic and model theory, and their applications to algebra and geometry. This book was developed from a series of lectures given by the author at the Mathematical Sciences Research Institute in 1998.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 342

Добавлена в каталог: 08.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\kappa, \lambda)$-model      151
$\aleph_{1}$-like ordering      165
$\kappa$-categorical theory      207
$\kappa$-homogeneous model      133
$\kappa$-saturation      138
$\kappa$-stable      135
$\mathcal{L}_{\kappa, \omega}$      57
$\mathcal{M}^{eq}$      28
$\omega$-stable      136 207
Abelian variety      308
Abramovich, D.      313
algebraic      30 208
Algebraic closure      208
Algebraic group      251 270
Algebraic group linear      24 252
Algebraically prime models      78
Amalgamation      106
Analytic      163
Artin, E.      93 99 112 323
Atomic diagram      44
Average of indiscernibles      247
Ax, J.      68 69 112
Axiom of Choice      315
Axiomatization      29
Axiomatization universal      47
Axioms      14
Back-and-forth construction      49
Back-and-forth system      67
Bad group      287
Baldwin — Lachlan Theorem      215
Baldwin, J.      207 213 215 288
Barwise, J.      172
Basis      290
Bennett, J.      32
Blum, L.      111 172 249
Borel, A.      68
Buechler, S.      173
Buium, A.      308
Burgess, J.      173
Canonical base      294
Cantor — Bendixson derivative      245
Cantor, G.      48
Cardinal      318
Cardinal inaccessible      319
Cardinal regular      319
Cardinal singular      319
Cardinal strongly inaccessible      320
Categoricity Theorem      207
cells      102
Center      259
Chain      47
Chain elementary      47
Chang, C.C.      69 173
Chatzidakis, Z.      69
Cherlin — Zil'ber Conjecture      252 287
Cherlin, G.      252 287 288
Chevalley, C.      88
Closed set in pregeometry      289
Closed unbounded set      189
Cofinality      319
Collins, G.      112
Compactness Theorem      34
Completeness theorem      34
Complex manifold      311
Complex torus      312
Connected component      254
Connected group      254
Constructible model      236
Constructible set      86 88
Construction      236
Continuum Hypothesis      320
Countable set      318
Davis, M.      21 71
Definable set      19
Definable set over A      19
Definable type      229
Definably interpreted      24
Derivation      148
Diagonal indiscernibles      198
Diagonal intersection      190
Diagram atomic      44
Diagram elementary      44
Diagram, F-diagram      161
Differential closure      171 240
Differentially algebraic      149
Differentially closed field      171 240 245 246 307 308
Differentially transcendental      149
DIMENSION      211 290
Dimension in Noetherian topology      306
Diophantine geometry      308
Divisible hull      76
Domain      8
Dubois, D.      111
Ehrenfeucht — Fraisse game      53
Ehrenfeucht — Mostowski models      180
Ehrenfeucht, A.      69 205
Elementary chain      47
Elementary class      14
Elementary diagram      44
Elementary embedding      44
Elementary equivalence      13
Elementary extension      44
Elementary substructure      44
Elliptic curve      252
Embedding      8
Embedding partial      49 52
Engler, E.      173
Erdos — Rado Theorem      177
Ersov, Y.      112
Exchange Principle      106
Existentially closed structure      63 105
expansion      31
Expansion by definitions      31
Extension      9
Fagin, R.      68
Faltings, G.      312
Field real      94
Field real closed      94
Filter      63
Filter Frechet      63
Filter principal      63
Filter ultrafilter      64
Finite Equivalence Relation Theorem      247
Fischer, M.      112
forking      228
Formula atomic      10
Formula positive      107
Fragment      158
Fraisse constructions      68
Fraisse, R.      69
Friedman, H.      172
Generic filter      321
Generic point      227
Generic type      256
Geometry      290
Goedel, K.      34 68 84 195
Group bounded exponent      157
group configuration      284
Group locally finite      157
Harnik, V.      249
Harrington, L.      196
Hasse, H.      65
Henkin construction      35 39 65
Henkin, L.      35 39 171
Hodges, W.      248
Homogeneous model      133
Hrushovski, E.      282 284 292 300 302 307 308
Inaccessible      319
Indecomposable      261
Independence      209 234 290
Independent      290
Indiscernible k-tuples      248
Indiscernibles      210
Indiscernibles diagonal      198
Indiscernibles type      181
Interpretable structure      27
Interpretation pure      31
Isolated type      120
Isomorphism      9
Jensen, R.      173
Kanamori, A.      196 205
Karp, C.      57 69
Keisler, H.J.      69 172
Ketonen, J.      205
Kochen, S.      112
Koenig's lemma      321
Kolchin closed set      171
Kolchin, E.      249 274 277 288
Krivine, J.-L.,      111
Krull dimension      226
Lachlan, A.      207 213 215
Language      8
Language recursive      34
Lascar, D.      111 248 249 296
Lefschetz principle      42
Lindstrom, P.      69
Linear strongly minimal set      296
localization      290
Locally modular pregeometry      290
Logical consequence      18
Los, J.      64 68 69
Lowenheim — Skolem theorem      45 46
MacDowell, R.      171
Macintyre, A.      69 112 113 258 288
Malcev, A.      68
Manin, J.      308 313
Many-sorted structure      28
Marker, D.      112
Matijasevic, J.      21 71
Mayer, L.      173
McAloon, K.      196 205
McQuillen, M.      312
Mekler, A.      32
Miller, A.      173
Milnor, J.      101
Minimal formula      208
Minimal set      208
Mitchell, W.      173
Model      14
Model $\kappa$-homogeneous      133
Model $\kappa$-saturated      138
Model $\kappa$-universal      143
Model companion      106
Model complete theory      78 105
Model completion      106
Model homogeneous      133
Model prime      129
Model saturated      138
Modular pregeometry      290
Monster model      218
Mordell conjecture      312
Mordell — Lang Conjecture      309 312
Morley degree      220
Morley rank      215 218
Morley rank of definable set      218
Morley sequence      241
Morley, M.      69 158 172 205 207 213 248 249
Morphism      269
Mostowski, A.      69 205
Nilpotent group      267
Noetherian topology      305
Nullstellensatz      88
o-minimal theory      81
One-based theory      298
Open induction      110
Open mapping theorem      238 247
Order indiscernibles      179
Order property      221
Order type      317
Orderable field      93
Ordinal      316
Ordinal limit      317
Ordinal successor      317
Orey, S.      171
Overspill      61
Paris, J.      196
Peretjat'kin, M.      69
Peterzil, Y.      311
Picard — Vessiot extension      275
Pillay, A.      111 249 296 302 308 311 312
Poizat, B.      111 205 274 288
Polish space      173
Positive formula      107
Power set      5
Pregeometry      289
Pregeometry locally modular      290
Pregeometry modular      290
Pregeometry trivial      290
Presburger arithmetic      82 170
Presburger, M.      111
Prime model      129
Prime model extension      135
proof      33
Puiseux series      110
Putnam, H.      21 71
Quantifier depth      54
Quantifier elimination      71 72 148
Quantifier elimination positive      107
Quasirational function      89
Rabin, M.      112
Ramsey's theorem      175
Real closed field      94
Real field      94
Recursive saturation      169
Reduct      31
Regressive function      191
Regular cardinal      319
Reineke, J.      258 259
Ressayre, J-P.      236 249
Risler, J.-J.      111
Ritt — Raudenbusch Basis Theorem      171
Robinson, A.      68 99 111
Robinson, J.      21 71
Rosenlicht, M.      249
Rowbottom, F.      205
Rudin, W.      68
Ryll-Nardzewski, C.      173
Satisfaction      11
Saturated model      138
Saxl, J.      288
Scattered theory      159
Schanuel's conjecture      112
Schlipf, J.      172
Schreier, O.      93 323
Scott rank      59
Scott sentence      59
Scott set      170
Scott, D.      48 57 69
Seidenberg, A.      98
Semialgebraic set      98
Sentence      10
Shelah, S.      69 172 173 205 248 249 288
Shepherdson, J.      111
Silver, J.      173 205
Simply closed      78
Singular cardinal      319
Skolem Functions      45 101
Skolem functions invariant      101
Skolem hull      180
Skolem, T.      68
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