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Tokyo Metropolitan University Library

Logic and Structure

by Dirk van Dalen. -- 3rd ed. 1994. -- Springer Berlin Heidelberg, 1994. -- (Universitext). w. <EB00021314>
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Logic and Structure

by Dirk van Dalen. -- 3rd ed. 1994. -- Springer Berlin Heidelberg, 1994. -- (Universitext). w. <EB00021314>
Tag:
No tag is registered
Functions:
Details
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Bibliography Details

IDENT https://doi.org/10.1007/978-3-662-02962-6
title and statement of responsibility area Logic and Structure / by Dirk van Dalen
specific material designation code Remote
edition area 3rd ed. 1994
publication,distribution,etc.,area Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 1994
physical description area X, 220 p : online resource
Volume Information
ISBN 9783662029626
parent bibliography link Universitext <>//a
contents of works 0. Introduction
contents of works 1. Propositional Logic
contents of works 2. Predicate Logic
contents of works 3. Completeness and Applications
contents of works 4. Second Order Logic
contents of works 5. Intuitionistic Logic
contents of works 6. Normalisation
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
NCID 9783662029633
text language code English
author link *Dalen, Dirk van <> author
author link SpringerLink (Online service) <>
classification DC23:511.3
subject headings Mathematical logic
subject headings Mathematics—Study and teaching 
subject headings Mathematical Logic and Foundations
subject headings Mathematics Education
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