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: Finitely Supported Mathematics
    sub title: An Introduction
  name:
    name part: Alexandru, Andrei.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ciobanu, Gabriel.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VII, 185 p. online resource.
  abstract: In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets). In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set). It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion…
  table of contents: Introduction -- Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics -- Algebraic Structures in Finitely Supported Mathematics -- Extended Fraenkel-Mostowski Set Theory -- Process Calculi in Finitely Supported Mathematics -- References. .
  note: by Andrei Alexandru, Gabriel Ciobanu.
  subject:
    topic: Computer science
  subject:
    topic: Computers
  subject:
    topic: Computer science
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematical logic
  subject:
    topic: Computer Science
  subject:
    topic: Theory of Computation
  subject:
    topic: Mathematics of Computing
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Algebra
  classification: QA75.5-76.95
  classification: 004.0151
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319422824
  identifier: http://dx.doi.org/10.1007/978-3-319-42282-4
  record info:
    record creation date: 160726
    record change date: 20160726192141.0
    record identifier: 978-3-319-42282-4