rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Logic and Structure
  name:
    name part: Dalen, Dirk.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1994
    edition: Third, Augmented edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (x, 220 pages)
  abstract: 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.
  table of contents: Introduction -- Propositional Logic -- Predicate Logic -- Completeness and Applications -- Second Order Logic -- Intuitionistic Logic -- Normalisation.
  note: by Dirk Dalen.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Logic, Symbolic and mathematical
  subject:
    topic: Logic, Symbolic and mathematical
  subject:
    topic: Mathematics
  classification: QA8.9-10.3
  classification: 511.3
  related item:
    title info:
      title: Universitext
  identifier: 9783662029626 (electronic bk.)
  identifier: 3662029626 (electronic bk.)
  identifier: 9783540578390
  identifier: 3540578390
  identifier: 3662029626
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 130321
    record change date: 20260422164355.4
    record identifier: in00003559280
    language of cataloging:
      language term: eng