Skip to main content
SpringerLink
Log in
SpringerLink
Log in

On Primitive Recursive Realizabilities

  • Conference paper
Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

Included in the following conference series:

Abstract

An example of arithmetic sentence which is deducible in intuitionistic predicate calculus with identity but is not strictly primitive recursively realizable by Z. Damnjanovic is proposed. It is shown also that the notions of primitive recursive realizability by Z. Damnjanovic and by S. Salehi are essentially different.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Axt, P.: Enumeration and the Grzegorczyk hierarchy. Z. math. Logik und Grundl. Math. 9, 53–65 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  2. Damnjanovic, Z.: Strictly primitive recursive realizability. I. J. Symbol. Log. 59, 1210–1227 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Grzegorczyk, A.: Some classes of recursive functions. Rozprawy matematyczne 4, 1–46 (1953)

    MathSciNet  MATH  Google Scholar 

  4. Kleene, S.C.: On the interpretation of intuitionistic number theory. J. Symbol. Log. 10, 109–124 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kleene, S.C.: Extension of an effectively generated class of functions by enumeration. Colloquium Mathematicum 6, 67–78 (1958)

    MathSciNet  MATH  Google Scholar 

  6. Plisko, V.E.: On the relation between two notions of primitive recursive realizability. Vestnik Moskovskogo Universiteta. Ser. 1. Matematika. Mekhanika, N 1, 6–11 (2006)

    Google Scholar 

  7. Salehi, S.: A generalized realizability for constructive arithmetic. Bull. Symbol. Log. 7, 147–148 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    Valery Plisko

Authors
  1. Valery Plisko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Plisko, V. (2006). On Primitive Recursive Realizabilities. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_31

Download citation

  • DOI: https://doi.org/10.1007/11753728_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation