Model Theory : An IntroductionSpringer Science & Business Media, 21.08.2002 - 345 Seiten Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures |
Inhalt
Structures and Theories | 7 |
12 Theories | 14 |
13 Definable Sets and Interpretability | 19 |
Basic Techniques | 33 |
22 Complete Theories | 40 |
23 Up and Down | 44 |
24 Back and Forth | 48 |
25 Exercises and Remarks | 60 |
ωStable Theories | 206 |
62 Morley Rank | 215 |
63 Forking and Independence | 227 |
64 Uniqueness of Prime Model Extensions | 236 |
65 Morley Sequences | 240 |
66 Exercises and Remarks | 243 |
7 ωStable Groups | 251 |
72 Generic Types | 255 |
Algebraic Examples | 71 |
32 Algebraically Closed Fields | 84 |
33 Real Closed Fields | 93 |
34 Exercises and Remarks | 104 |
Realizing and Omitting Types | 114 |
42 Omitting Types and Prime Models | 125 |
43 Saturated and Homogeneous Models | 138 |
44 The Number of Countable Models | 155 |
45 Exercises and Remarks | 163 |
Indiscernibles | 175 |
52 Order Indiscernibles | 178 |
53 A ManyModels Theorem | 189 |
54 An Independence Result in Arithmetic | 195 |
55 Exercises and Remarks | 202 |
73 The Indecomposability Theorem | 261 |
74 Definable Groups in Algebraically Closed Fields | 267 |
75 Finding a Group | 279 |
76 Exercises and Remarks | 285 |
8 Geometry of Strongly Minimal Set | 289 |
82 Canonical Bases and Families of Plane Curves | 293 |
83 Geometry and Algebra | 300 |
84 Exercises and Remarks | 309 |
Set Theory | 314 |
Real Algebra | 323 |
References | 329 |
| 337 | |
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Häufige Begriffe und Wortgruppen
Abelian group acl(A algebraic group algebraically closed field automorphism axioms b₁ canonical base claim closed sets closure constant symbol constructible contradiction Corollary countable countable language countable models definable sets definable subgroup Definition differential field differentially closed differentially closed fields element elementary embedding elementary extension equivalence relation example Exercise finite Morley rank finitely satisfiable function symbol geometry homogeneous indecomposable induction interpret irreducible isolated type isomorphic L-formula L-sentence L-structure L-theory Lemma Let F limit ordinal linear order model theory Morley rank No-categorical No-saturated one-based order indiscernibles Peano arithmetic player polynomial Proof Let Proposition prove quantifier elimination quantifier-free formula real closed field realizes recursive RM(p saturated model semialgebraic Show Skolem Sn(T Stab(p strongly minimal strongly minimal set structure subset uncountable Vaughtian pair w-stable group w-stable theories w₁ Zariski closed