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: Recursive functionals
  name:
    name part: Sanchis, Luis E.
    role:
      role term: creator
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    place:
      place term: Amsterdam
    place:
      place term: New York
    publisher: North-Holland
    date issued: 1992
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xii, 277 pages) : illustrations
  abstract: This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.
  table of contents: Front Cover; Recursive Functionals; Copyright Page; Contents; Preface; Chapter 1. Mappings and Domains; Chapter 2. Functionals and Predicates; Chapter 3. Basic Operations; Chapter 4. Primitive Recursive Operations; Chapter 5. Basic Recursion; Chapter 6. Church's Thesis; Chapter 7. Functional Recursion; Chapter 8. Recursive Algorithms; Chapter 9. Formalization: Structural Semantics; Chapter 10. Formalization: Reductional Semantics; Chapter 11. Interpreters; Chapter 12. A Universal Interpreter; Chapter 13. Enumeration; Chapter 14. Continuous Functionals; Chapter 15. A Selector Theorem
  table of contents: Chapter 16. HyperenumerationChapter 17. Recursion in Normal Classes; Appendix Recursion and Church's Thesis; References; Index; List of Symbols
  note: Luis E. Sanchis.
  note: Includes bibliographical references (pages 265-267) and index.
  note: English.
  subject:
    topic: Recursive functions
  subject:
    topic: Fonctions récursives
  subject:
    topic: COMPUTERS
    topic: Machine Theory
  subject:
    topic: Recursive functions
  subject:
    topic: Fonctions récursives
  subject:
    topic: Mathematical logic
  classification: QA9.615 .S26 1992eb
  classification: 511.3/5
  related item:
    title info:
      title: Recursive functionals
    name:
      name part: Sanchis, Luis E.
    origin info:
      publisher: Amsterdam ; New York : North-Holland, 1992
    identifier: (DLC) 92010555
    identifier: (OCoLC)25628698
  related item:
    title info:
      title: Studies in logic and the foundations of mathematics ; v. 131
  identifier: 9780444894472
  identifier: 0444894470
  identifier: 9780080887173
  identifier: 0080887171
  identifier: 1281778834
  identifier: 9781281778833
  identifier: 9786611778835
  identifier: 6611778837
  identifier: 92010555
  identifier: 122102:125822 Elsevier Science & Technology
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 090320
    record change date: 20260326161330.0
    record identifier: in00005737035
    language of cataloging:
      language term: eng