Hodges, Wilfrid
A shorter model theory - New York Cambridge University Press 1997 - x, 310p.
Includes bibliographical references and indexes
Introduction vii (2)
Note on notation ix
1 Naming of parts
1 (20)
1.1 Structures
2 (3)
1.2 Homomorphisms and substructures
5 (5)
1.3 Terms and atomic formulas
10 (5)
1.4 Parameters and diagrams
15 (2)
1.5 Canonical models
17 (3)
Further reading
20 (1)
2 Classifying structures
21 (48)
2.1 Definable subsets
22 (8)
2.2 Definable classes of structures
30 (7)
2.3 Some notions from logic
37 (6)
2.4 Maps and the formulas they preserve
43 (5)
2.5 Classifying maps by formulas
48 (3)
2.6 Translations
51 (8)
2.7 Quantifier elimination
59 (9)
Further reading
68 (1)
3 Structures that look alike
69 (24)
3.1 Theorems of Skolem
69 (4)
3.2 Back-and-forth equivalence
73 (9)
3.3 Games for elementary equivalence
82 (9)
Further reading
91 (2)
4 Interpretations
93 (31)
4.1 Automorphisms
94 (7)
4.2 Relativisation
101 (6)
4.3 Interpreting one structure in another
107 (6)
4.4 Imaginary elements
113 (9)
Further reading
122 (2)
5 The first-order case: compactness
124 (34)
5.1 Compactness for first-order logic
124 (6)
5.2 Types
130 (4)
5.3 Elementary amalgamation
134 (7)
5.4 Amalgamation and preservation
141 (6)
5.5 Expanding the language
147 (5)
5.6 Indiscernibles
152 (4)
Further reading
156 (2)
6 The countable case
158 (24)
6.1 Fraisse's construction
158 (7)
6.2 Omitting types
165 (6)
6.3 Countable categoricity
171 (4)
6.4 w-categorical structures by Fraisse's method
175 (6)
Further reading
181 (1)
7 The existential case
182 (28)
7.1 Existentially closed structures
183 (5)
7.2 Constructing e.c. structures
188 (7)
7.3 Model-completeness
195 (6)
7.4 Quantifier elimination revisited
201 (7)
Further reading
208 (2)
8 Saturation
210 (40)
8.1 The great and the good
211 (9)
8.2 Big models exist
220 (5)
8.3 Syntactic characterisations
225 (8)
8.4 One-cardinal and two-cardinal theorems
233 (4)
8.5 Ultraproducts and ultrapowers
237 (11)
Further reading
248 (2)
9 Structure and categoricity
250 (48)
9.1 Ehrenfeucht-Mostowski models
251 (6)
9.2 Minimal sets
257 (7)
9.3 Totally transcendental structures
264 (9)
9.4 Stability
273 (13)
9.5 Morley's theorem
286 (10)
Further reading
296 (2)
Index to symbols 298 (2)
Index 300
0521587131
Model theory
510.6 / HOD
A shorter model theory - New York Cambridge University Press 1997 - x, 310p.
Includes bibliographical references and indexes
Introduction vii (2)
Note on notation ix
1 Naming of parts
1 (20)
1.1 Structures
2 (3)
1.2 Homomorphisms and substructures
5 (5)
1.3 Terms and atomic formulas
10 (5)
1.4 Parameters and diagrams
15 (2)
1.5 Canonical models
17 (3)
Further reading
20 (1)
2 Classifying structures
21 (48)
2.1 Definable subsets
22 (8)
2.2 Definable classes of structures
30 (7)
2.3 Some notions from logic
37 (6)
2.4 Maps and the formulas they preserve
43 (5)
2.5 Classifying maps by formulas
48 (3)
2.6 Translations
51 (8)
2.7 Quantifier elimination
59 (9)
Further reading
68 (1)
3 Structures that look alike
69 (24)
3.1 Theorems of Skolem
69 (4)
3.2 Back-and-forth equivalence
73 (9)
3.3 Games for elementary equivalence
82 (9)
Further reading
91 (2)
4 Interpretations
93 (31)
4.1 Automorphisms
94 (7)
4.2 Relativisation
101 (6)
4.3 Interpreting one structure in another
107 (6)
4.4 Imaginary elements
113 (9)
Further reading
122 (2)
5 The first-order case: compactness
124 (34)
5.1 Compactness for first-order logic
124 (6)
5.2 Types
130 (4)
5.3 Elementary amalgamation
134 (7)
5.4 Amalgamation and preservation
141 (6)
5.5 Expanding the language
147 (5)
5.6 Indiscernibles
152 (4)
Further reading
156 (2)
6 The countable case
158 (24)
6.1 Fraisse's construction
158 (7)
6.2 Omitting types
165 (6)
6.3 Countable categoricity
171 (4)
6.4 w-categorical structures by Fraisse's method
175 (6)
Further reading
181 (1)
7 The existential case
182 (28)
7.1 Existentially closed structures
183 (5)
7.2 Constructing e.c. structures
188 (7)
7.3 Model-completeness
195 (6)
7.4 Quantifier elimination revisited
201 (7)
Further reading
208 (2)
8 Saturation
210 (40)
8.1 The great and the good
211 (9)
8.2 Big models exist
220 (5)
8.3 Syntactic characterisations
225 (8)
8.4 One-cardinal and two-cardinal theorems
233 (4)
8.5 Ultraproducts and ultrapowers
237 (11)
Further reading
248 (2)
9 Structure and categoricity
250 (48)
9.1 Ehrenfeucht-Mostowski models
251 (6)
9.2 Minimal sets
257 (7)
9.3 Totally transcendental structures
264 (9)
9.4 Stability
273 (13)
9.5 Morley's theorem
286 (10)
Further reading
296 (2)
Index to symbols 298 (2)
Index 300
0521587131
Model theory
510.6 / HOD