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: Function Algebras on Finite Sets
    sub title: A Basic Course on Many-Valued Logic and Clone Theory
  name:
    name part: Lau, Dietlinde.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 670 p. online resource.
  abstract: Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.
  table of contents: Preliminaries -- Preliminaries -- Universal Algebra -- Basic Concepts of Universal Algebra -- Lattices -- Hull Systems and Closure Operators -- Homomorphisms, Congruences, and Galois Connections -- Direct and Subdirect Products -- Varieties, Equational Classes, and Free Algebras -- Function Algebras -- Basic Concepts, Notations, and First Properties -- The Galois-Connection Between Function- and Relation-Algebras -- The Subclasses of P2 -- The Subclasses of Pk Which Contain Pk1 -- The Maximal Classes of Pk -- Rosenberg’s Completeness Criterion for Pk -- Further Completeness Criteria -- Some Properties of the Lattice -- Congruences and Automorphisms on Function Algebras -- The Relation Degree and the Dimension of Subclasses of Pk -- On Generating Systems and Orders of the Subclasses of Pk -- Subclasses of Pk,2 -- Classes of Linear Functions -- Submaximal Classes of P3 -- Finite and Countably Infinite Sublattices of Depth 1 or 2 of -- The Maximal Classes of ?a?Q Polka for Q Ek -- Maximal Classes of PolkEl for 2 ? l < k -- Further Submaximal Classes of Pk -- Minimal Classes and Minimal Clones of Pk -- Partial Function Algebras.
  note: by Dietlinde Lau.
  subject:
    topic: Mathematics
  subject:
    topic: Arithmetic and logic units, Computer
  subject:
    topic: Algebra
  subject:
    topic: Mathematical logic
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Arithmetic and Logic Structures
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9783540360230
  identifier: http://dx.doi.org/10.1007/3-540-36023-9
  record info:
    record creation date: 100301
    record change date: 20151204180446.0
    record identifier: 978-3-540-36023-0