Skip to main content

Calculability of the primitive recursive functionals of finite type over the natural numbers

A revised version

  • Conference paper
  • First Online:
⊨ISILC Proof Theory Symposion

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 500))

  • 273 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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

  • G. Gentzen 1935 Untersuchungen über das logische Schliessen. I. II. Mathematische Zeitschrift 39, pp. 176–210, 405–431.

    Article  MathSciNet  MATH  Google Scholar 

  • K. Gödel 1958 Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica 12, pp. 280–287.

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Hanatani 1966 Calculabilité des fonctionnelles récursives primitives de type fini sur les nombres naturels. Annals of the Japan Association for Philosophy of Science, Vol. 3 No. 1, pp. 19–30.

    Article  MathSciNet  MATH  Google Scholar 

  • S. Hinata 1967 Calculability of primitive recursive functionals of finite type. Science reports of the Tokyo Kyoiku Daigaku, Section A, Vol. 9, No. 226, pp. 42–59.

    MathSciNet  Google Scholar 

  • D. Prawitz 1971 Ideas and results in proof theory. Proceedings of the Second Scandinavian Logic Symposium. Ed. by J.E. Fenstad. Amsterdam-London (North-Holland Publ. Co.), pp. 235–307.

    Google Scholar 

  • W. W. Tait 1967 Intensional interpretations of functionals of finite type I. Journal of symbolic Logic, 32, pp. 198–212.

    Article  MathSciNet  MATH  Google Scholar 

  • W. W. Tait 1971 Normal form theorem for bar recursive functions of finite type. Proceedings of the Second Scandinavian Logic Symposium. Ed. by J.E. Fenstad. Amsterdam-London (North-Holland Publ. Co.), pp. 353–367.

    Google Scholar 

  • G. Takeuti 1955 On the fundamental conjecture of GLC I. Journal of the Mathematical Society of Japan, 7, pp. 249–275.

    Article  MathSciNet  MATH  Google Scholar 

  • A. S. Troelstra 1973 Metamathematical Investigation of intuitionistic Arithmetic and Analysis. Springer Lecture Notes Vol. 344. Berlin-Heidelberg-New York. *** DIRECT SUPPORT *** A00J4136 00004

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Justus Diller Gert H. Müller

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Hanatani, Y. (1975). Calculability of the primitive recursive functionals of finite type over the natural numbers. In: Diller, J., Müller, G.H. (eds) ⊨ISILC Proof Theory Symposion. Lecture Notes in Mathematics, vol 500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079550

Download citation

  • DOI: https://doi.org/10.1007/BFb0079550

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07533-2

  • Online ISBN: 978-3-540-38020-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics