| 1Introduction 1.1 Outline of the book 1.2 Assumed knowledge 2 Propositions and truth assignments 2.1 Introduction 2.2 The construction of propositional formulas 2.3 The interpretation of propositional formulas 2.4 Logical equivalence 2.5 The expressive power of connectives 2.6 Logical consequence 3 Formal propositional calculus 3.1 Introduction 3.2 A formal system for propositional calculus 3.3 Soundness and completeness 3.4 Independence of axioms and alternative systems 4 Predicates and models 4.1 Introduction: basic ideas 4.2 First-order languages and their interpretation 4.3 Universally valid formulas and logical equivalence 4.4 Some axiom systems and their consequences 4.5 Substructures and Isomorphisms 5 Formal predicate calculus 5.1 Introduction 5.2 A formal system for predicate calculus 5.3 The soundness theorem 5.4 The equality axioms and non-normal structures 5.5 The completeness theorem 6 Some uses of compactness 6.1 Introduction: the compactness theorem 6.2 Finite axiomatizability 6.3 Some non-axiomatizable theories 6.4 The Lowenheim-Skolem theorems 6.5 New models from old ones 6.6 Decidable theories Bibliography Index |
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