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: Turing Computability
    sub title: Theory and Applications
  name:
    name part: Soare, Robert I.
    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: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXXVI, 263 p. 4 illus. online resource.
  abstract: Turing's famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This model led to both the development of actual computers and to computability theory, the study of what machines can and cannot compute. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic. The author presents the subject as an art to be practiced, and an art in the aesthetic sense of inherent beauty which all mathematicians recognize in their subject. Part I gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic. Part II includes the study of computably open and closed sets of reals and basis and nonbasis theorems for effectively closed sets. Part III covers minimal Turing degrees. Part IV is an introduction to games and their use in proving theorems. Finally, Part V offers a short history of computability theory. The author is a leading authority on the topic and he has taught the subject using the book content over decades, honing it according to experience and feedback from students, lecturers, and researchers around the world. Most chapters include exercises, and the material is carefully structured according to importance and difficulty. The book is suitable for advanced undergraduate and graduate students in computer science and mathematics and researchers engaged with computability and mathematical logic.
  table of contents: Part I Foundations of Computability -- Chap. 1 Defining Computability -- Chap. 2 Computably Enumerable Sets -- Chap. 3 Turing Reducibility -- Chap. 4 The Arithmetical Hierarchy -- Chap. 5 Classifying C.E. Sets -- Chap. 6 Oracle Constructions and Forcing -- Chap. 7 The Finite Injury Method -- Part II Trees and Π01 Classes -- Chap. 8 Open and Closed Classes -- Chap. 9 Basis Theorems -- Chap. 10 Peano Arithmetic and Π01-Classes -- Chap. 11 Randomness and Π01-Classes -- Part III Minimal Degrees -- Chap. 12 Minimal Degrees Below Øʹʹ -- Chap. 13 Minimal Degrees Below Øʹ -- Part IV Games in Computability Theory -- Chap. 14 Banach-Mazur Games -- Chap. 15 Gale-Stewart Games -- Chap. 16 More Lachlan Games -- Part V History of Computability -- Chap. 17 History of Computability -- References -- Index.
  note: by Robert I. Soare.
  subject:
    topic: Computer science
  subject:
    topic: Computers
  subject:
    topic: Computer science
    topic: Mathematics
  subject:
    topic: Mathematical logic
  subject:
    topic: Computer Science
  subject:
    topic: Theory of Computation
  subject:
    topic: Mathematics of Computing
  subject:
    topic: Mathematical Logic and Foundations
  classification: QA75.5-76.95
  classification: 004.0151
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Theory and Applications of Computability, In cooperation with the association Computability in Europe
  identifier: 9783642319334
  identifier: http://dx.doi.org/10.1007/978-3-642-31933-4
  record info:
    record creation date: 160620
    record change date: 20160620144519.0
    record identifier: 978-3-642-31933-4