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Field name	Details
Dewey Class	511.3
Title	Logic and Structure ([EBook] /) / by Dirk van Dalen.
Author	Dalen, Dirk van
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1983.
Physical Details	X, 210 p. : online resource.
Series	Universitext 0172-5939
ISBN	9783662023822
Summary Note	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-Löwenheim, 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 Gödel 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 `normalization'. 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 Gödel'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.:
Contents note	0. Introduction -- 1. Propositional Logic -- 2. Predicate Logic -- 3. Completeness and Applications -- 4. Second-Order Logic -- 5. Intuitionistic Logic -- 6. Appendix -- 7. Bibliography -- 8. Gothic Alphabet -- 9. Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02382-2
Links to Related Works	Subject References: Mathematical logic . Mathematical Logic and Foundations . Mathematics . Authors: Dalen, Dirk van . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 511.3 .

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Logic and Structure

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