Logic and Structure
Dalen, Dirk van.
Logic and Structure [electronic resource] / by Dirk van Dalen. - 5th ed. 2013. - X, 263 p. 27 illus. online resource. - Universitext, 0172-5939 . - Universitext, .
Introduction -- Propositional Logic -- Predicate Logic -- Completeness and Applications -- Second Order Logic -- Intuitionistic Logic -- Normalization -- Gödel's theorem.
Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.
9781447145585
10.1007/978-1-4471-4558-5 doi
Mathematics.
Mathematical logic.
Mathematics.
Mathematical Logic and Foundations.
QA8.9-10.3
511.3
Logic and Structure [electronic resource] / by Dirk van Dalen. - 5th ed. 2013. - X, 263 p. 27 illus. online resource. - Universitext, 0172-5939 . - Universitext, .
Introduction -- Propositional Logic -- Predicate Logic -- Completeness and Applications -- Second Order Logic -- Intuitionistic Logic -- Normalization -- Gödel's theorem.
Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.
9781447145585
10.1007/978-1-4471-4558-5 doi
Mathematics.
Mathematical logic.
Mathematics.
Mathematical Logic and Foundations.
QA8.9-10.3
511.3