| Introduction 1 Propositional Logic 1.1 Propositions and Connectives 1.2 Semantics 1.3 Some Properties of Propositional logic 1.4 Natural Deduction 1.5 Completeness 1.6 The Missing Connectives 2 Predicate Logic 2.1 Quantifiers 2.2 Structurest 2.3 The Language of a Similarity Type 2.4 Semantics 2.5 Simple Properties of Predicate Logic 2.6 Identity 2.7 Examples 2.8 Natural Deduction 2.9 Adding the Existential Quantifier 2.10 Natural Deduction and Identity 3 Completeness and Applications 3.1 The Completeness Theorem 3.2 Compactness and Skolem-LSwenheim 3.3 Some Model Theory 3.4 Skolem Functions or How to Enrich Your Language 4 Second Order Logic 5 Intuitionistic Logic 5.1 Constructive Reasoning 5.2 Intuitionistic Propositional and Predicate Logic 5.3 Kripke Semantics 5.4 Some Model Theory 6 Normalisation 6.1 Cuts 6.2 Normalization for Classical Logic 6.3 Normalization for Intuitionistic Logic 7 G6del’S theorem 7.1 Primitive recursive flllnctions 7.2 Partial Recursive Functions 7.3 Recursively enumerable sets 7.4 Some arithmetic 7.5 Representability 7.6 Derivability 7.7 Incompleteness Bibliography Index |
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