A Course In Model Theory: An Introduction To Contemporary Mathematical Logic

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• Series: Universitext

• Year: 2,000

• Edition: 1

• Pages: 476

• Pages In File: 476

• Language: English

• Topic: 130

• Identifier: 0387986553,9780387986555

• Ddc: 512

• Paginated: 1

• Org File Size: 37,091,680

• Extension: pdf

• Toc: Cover......Page 1 Series......Page 3 More books of this Series......Page 476 Title......Page 4 Copyright......Page 5 Preface to the English Edition......Page 8 History of a Publication......Page 11 Contents......Page 18 Introduction......Page 24 1.1 Local Isomorphisms Between Relations......Page 33 1.2 Examples......Page 37 1.3 Infinite Back-and-Forth......Page 43 1.4 Historic and Bibliographic Notes......Page 45 2.1 Formulas......Page 47 2.2 Connections to the Back-and-Forth Technique......Page 55 2.3 Models and Theories......Page 57 2.4 Elementary Extensions: Tarski's Test, Löwenheim’s Theorem......Page 59 2.5 Historic and Bibliographic Notes......Page 61 3.1 Multirelations, Relational Structures......Page 63 3.2 Functions......Page 65 3.3 Löwenheim’s Theorem Revisited......Page 68 3.4 Historic and Bibliographic Notes......Page 69 4.1 Ultraproducts......Page 70 4.2 Compactness, Löwenheim-Skolem Theorem, Theorem of Common Elementary Extensions......Page 74 4.3 Henkin’s Method......Page 79 4.4 Historic and Bibliographic Notes......Page 84 5.1 Spaces of Types......Page 87 5.2 ω-Saturated Models......Page 89 5.3 Quantifier Elimination......Page 92 5.4 Historic and Bibliographic Notes......Page 95 6.1 Algebraically Closed Fields......Page 96 6.2 Differentially Closed Fields......Page 102 6.3 Boolean Algebras......Page 110 6.4 Ultrametric Spaces......Page 118 6.5 Modules and Existentially Closed Modules......Page 123 6.6 Real Closed Fields (not in the original edition)......Page 130 6.7 Historic and Bibliographic Notes......Page 137 7.1 The Successor Function......Page 140 7.2 The Order......Page 142 7.3 The Sum......Page 143 7.4 Sum and Product: Coding of Finite Sets......Page 148 7.5 Coding of Formulas; Tarski’s Theorem......Page 154 7.6 The Hierarchy of Arithmetic Sets......Page 156 7.7 Some Axioms, Models, and Fragments of Arithmetic......Page 166 7.8 Nonstandard Models with Arithmetic Definitions......Page 173 7.9 Arithmetic Translation of Henkin’s Method......Page 174 7.10 The Notion of Proof; Decidable Theories......Page 179 7.11 Gödel’s Theorem......Page 183 7.12 A Little Mathematical Fiction......Page 187 7.13 Historic and Bibliographic Notes......Page 190 8.1 Well-Ordered Sets......Page 192 8.2 Axiom of Choice......Page 196 8.3 Cardinals......Page 203 8.4 Cofinality......Page 209