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: Ordered Sets
  name:
    name part: Harzheim, Egbert.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2005
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 386 p. online resource.
  abstract: The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory.
  table of contents: Fundamental notions of set theory -- Fundamental notions -- General relations between posets and their chains and antichains -- Linearly ordered sets -- Products of orders -- Universally ordered sets -- Applications of the splitting method -- The dimension of posets -- Well-founded posets, pwo-sets and trees -- On the order structure of power sets -- Comparison of order types -- Comparability graphs.
  note: by Egbert Harzheim.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Ordered algebraic structures
  subject:
    topic: Mathematics
  subject:
    topic: Order, Lattices, Ordered Algebraic Structures
  classification: QA172-172.4
  classification: QA171.5
  classification: 511.33
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Advances in Mathematics ; 7
  identifier: 9780387242224
  identifier: http://dx.doi.org/10.1007/b104891
  record info:
    record creation date: 100301
    record change date: 20151103123424.0
    record identifier: 978-0-387-24222-4