A shorter model theory

By: Hodges, WilfridMaterial type: TextTextLanguage: English Publication details: New York Cambridge University Press 1997Description: x, 310pISBN: 0521587131Subject(s): Model theory | Mathematics
Contents:
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
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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

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