## 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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### Contents

Introduction | 2 |

Predicate Logic | 57 |

Completeness and Applications | 103 |

Second Order Logic | 143 |

Intuitionistic Logic | 153 |

Normalisation | 187 |

Gödels theorem | 209 |

257 | |

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### Common terms and phrases

algebra apply argument arithmetic atoms axioms bound called cardinality closed complete computation connectives consider consistent constants construction contains Contradiction convenient converse Corollary course decidable deﬁned Deﬁnition derivation effective elements elimination equivalence example Exercise exists extension fact finite ﬁrst formula give given hence holds identity immediately interpretation introduce intuitionistic logic Kripke language Lemma look mathematics maximal means natural node normal notation Note notion Observe obtained occur partial recursive positive precise predicate logic prime primitive recursive Proof properties propositional logic propositions prove quantiﬁer reader reason recursive functions relation replaced result rule second-order sentences sequence Show simple Skolem standard step structures substitution Suppose symbols Theorem theory true truth universal valuation variables write