Toc: Cover......Page 1Series......Page 3More books of this Series......Page 476Title......Page 4Copyright......Page 5Preface to the English Edition......Page 8History of a Publication......Page 11Contents......Page 18Introduction......Page 241.1 Local Isomorphisms Between Relations......Page 331.2 Examples......Page 371.3 Infinite Back-and-Forth......Page 431.4 Historic and Bibliographic Notes......Page 452.1 Formulas......Page 472.2 Connections to the Back-and-Forth Technique......Page 552.3 Models and Theories......Page 572.4 Elementary Extensions: Tarski's Test, Löwenheim’s Theorem......Page 592.5 Historic and Bibliographic Notes......Page 613.1 Multirelations, Relational Structures......Page 633.2 Functions......Page 653.3 Löwenheim’s Theorem Revisited......Page 683.4 Historic and Bibliographic Notes......Page 694.1 Ultraproducts......Page 704.2 Compactness, Löwenheim-Skolem Theorem, Theorem of Common Elementary Extensions......Page 744.3 Henkin’s Method......Page 794.4 Historic and Bibliographic Notes......Page 845.1 Spaces of Types......Page 875.2 ω-Saturated Models......Page 895.3 Quantifier Elimination......Page 925.4 Historic and Bibliographic Notes......Page 956.1 Algebraically Closed Fields......Page 966.2 Differentially Closed Fields......Page 1026.3 Boolean Algebras......Page 1106.4 Ultrametric Spaces......Page 1186.5 Modules and Existentially Closed Modules......Page 1236.6 Real Closed Fields (not in the original edition)......Page 1306.7 Historic and Bibliographic Notes......Page 1377.1 The Successor Function......Page 1407.2 The Order......Page 1427.3 The Sum......Page 1437.4 Sum and Product: Coding of Finite Sets......Page 1487.5 Coding of Formulas; Tarski’s Theorem......Page 1547.6 The Hierarchy of Arithmetic Sets......Page 1567.7 Some Axioms, Models, and Fragments of Arithmetic......Page 1667.8 Nonstandard Models with Arithmetic Definitions......Page 1737.9 Arithmetic Translation of Henkin’s Method......Page 1747.10 The Notion of Proof; Decidable Theories......Page 1797.11 Gödel’s Theorem......Page 1837.12 A Little Mathematical Fiction......Page 1877.13 Historic and Bibliographic Notes......Page 1908.1 Well-Ordered Sets......Page 1928.2 Axiom of Choice......Page 1968.3 Cardinals......Page 2038.4 Cofinality......Page 209