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A shorter model theory / Wilfrid Hodges.

By: Hodges, Wilfrid.
Material type: materialTypeLabelBookPublisher: Cambridge ; New York : Cambridge University Press, 1997Description: x, 310 p. : ill. ; 23 cm.ISBN: 0521587131 (pbk.).Subject(s): Model theoryOther classification: 03Cxx (03-01) Online resources: Publisher description
Contents:
Introduction vii -- Note on notation ix -- 1 Naming of parts [1] -- 1.1 Structures [2] -- 1.2 Homomorphisms and substructures [5] -- 1.3 Terms and atomic formulas [10] -- 1.4 Parameters and diagrams [15] -- 1.5 Canonical models [17] -- Further reading [20] -- 2 Classifying structures [21] -- 2.1 Definable subsets [22] -- 2.2 Definable classes of structures [30] -- 2.3 Some notions from logic [37] -- 2.4 Maps and the formulas they preserve [43] -- 2.5 Classifying maps by formulas [48] -- 2.6 Translations [51] -- 2.7 Quantifier elimination [59] -- Further reading [68] -- 3 Structures that look alike [69] -- 3.1 Theorems of Skolem [69] -- 3.2 Back-and-forth equivalence [73] -- 3.3 Games for elementary equivalence [82] -- Further reading [91] -- 4 Interpretations [93] -- 4.1 Automorphisms [94] -- 4.2 Relativisation [101] -- 4.3 Interpreting one structure in another [107] -- 4.4 Imaginary elements [113] -- Further reading [122] -- 5 The first-order case: compactness [124] -- 5.1 Compactness for first-order logic [124] -- 5.2 Types [130] -- 5.3 Elementary amalgamation [134] -- 5.4 Amalgamation and preservation [141] -- 5.5 Expanding the language [147] -- 5.6 Indiscernibles [152] -- Further reading [156] -- 6 The countable case [158] -- 6.1 Fraïssé’s construction [158] -- 6.2 Omitting types [165] -- 6.3 Countable categoricity [171] -- 6.4 w-categorical structures by Fraïssé’s method 175 Further reading [181] -- 7 The existential case [182] -- 7.1 Existentially closed structures [183] -- 7.2 Constructing e.c. structures [188] -- 7.3 Model-completeness [195] -- 7.4 Quantifier elimination revisited [201] -- Further reading [208] -- 8 Saturation [210] -- 8.1 The great and the good [211] -- 8.2 Big models exist [220] -- 8.3 Syntactic characterisations [225] -- 8.4 One-cardinal and two-cardinal theorems [233] -- 8.5 Ultraproducts and ultrapowers 237 Further reading [248] -- 9 Structure and categoricity [250] -- 9.1 Ehrenfeucht-Mostowski models [251] -- 9.2 Minimal sets [257] -- 9.3 Totally transcendental structures [264] -- 9.4 Stability [273] -- 9.5 Morley’s theorem [286] -- Further reading [296] -- Index to symbols [298] -- Index [300] --
Summary: "This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading."--Contratapa.
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Incluye referencias bibliográficas e índices.

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

MR, MR1462612

"This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading."--Contratapa.

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