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Author Dalen, Dirk van. author Logic and Structure [electronic resource] / by Dirk van Dalen Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994 Third, Augmented Edition http://dx.doi.org/10.1007/978-3-662-02962-6 X, 220 p. online resource

SUMMARY

A book which efficiently presents the basics of propositional and predicate logic, van Dalen's popular textbook contains a complete treatment of elementary classical logic, using Gentzen's Natural Deduction. Propositional and predicate logic are treated in separate chapters in a leisured but precise way. Chapter Three presents the basic facts of model theory, e.g. compactness, Skolem-Lรถwenheim, elementary equivalence, non-standard models, quantifier elimination, and Skolem functions. The discussion of classical logic is rounded off with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, one chapter is devoted to intuitionistic logic. Completeness is established for Kripke semantics. A number of specific constructive features, such as apartness and equality, the Gรถdel translation, the disjunction and existence property have been incorporated. The power and elegance of natural deduction is demonstrated best in the part of proof theory called ̀cut-elimination' or ǹormalization'. Chapter 6 is devoted to this topic; it contains the basic facts on the structure of derivations, both classically and intuitionistically. Finally, this edition contains a new chapter on Gรถdel's first incompleteness theorem. The chapter is self-contained, it provides a systematic exposition of primitive recursion and partial recursive functions, recursive by enumerable sets, and recursive separability. The arithmetization of Peano's arithmetic is based on the natural deduction system

CONTENT

0. Introduction -- 1. Propositional Logic -- 2. Predicate Logic -- 3. Completeness and Applications -- 4. Second Order Logic -- 5. Intuitionistic Logic -- 6. Normalisation

Mathematics Mathematical logic Mathematics -- Study and teaching Mathematics Mathematical Logic and Foundations Mathematics Education

Location

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