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International Computer Science Symposium in Russia

CSR 2006: Computer Science – Theory and Applications pp 304–312Cite as

On Primitive Recursive Realizabilities

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

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.

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References

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

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  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)

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

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Author information

Authors and Affiliations

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

    Valery Plisko

Authors
  1. Valery Plisko
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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

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© 2006 Springer-Verlag Berlin Heidelberg

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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

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  • 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)

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