## Logic and structureFrom the reviews "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary |

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#### Review: Logic and Structure

User Review - Liam Kofi - GoodreadsExcellent intermediate level textbook. I'm an evangelist for this book. Read full review

#### Review: Logic and Structure

User Review - Liam Kofi - GoodreadsExcellent intermediate level textbook. I'm an evangelist for this book. Read full review

### Contents

Introduction | 1 |

Predicate Logic | 55 |

Completeness and Applications | 103 |

Copyright | |

4 other sections not shown

### Common terms and phrases

algebra apply arithmetic atoms axioms called cardinality Completeness Theorem connectives consider constant symbols construction contains converse Corollary defined Definition densely ordered disjunction elements elimination rule example Exercise existential fclh finitely axiomatisable first-order logic formation sequences free variables function symbols hence Henkin theory identity Induction hypothesis infinite introduce intuitionistic logic isomorphic Kripke model language mathematics maximally consistent Mod(A Mod(r Model Existence Lemma model theory natural deduction natural numbers negation node non-standard model normal derivation normal form normalisation notation Note notion obtained occur partially ordered set predicate logic predicate symbol prenex prenex normal form Proof PROP properties propositional logic prove quantifier reader recursion relation result satisfying second-order logic semantics sentences Show Skolem function strictly positive structures subformula subset Substitution Theorem substructure Suppose syntactical true truth table valuation Vx(x Vxy(x