Skip to main content

The Hahn-Banach theorem and a restricted inductive definition

  • Conference paper
  • First Online:
Logic Symposia Hakone 1979, 1980

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 891))

  • 260 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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
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. W. Ackermann, Konstruktiver Aufbau eines Abschnitts der zweiter Cantorschen Zahlenklasse, Math. Zeit. 53 (1951), 403–413.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Banach, Theóries des Opérations Lineares, Chealsea Publ. Co., N.Y. (1955).

    Google Scholar 

  3. E. Bishop, Foundations of Constructive Analysis, McGraw-Hill Book Co., N.Y. (1967).

    MATH  Google Scholar 

  4. E. Bishop, Mathematics as a numerical language, Intuitionism and Proof Theory, edited by J. Myhill, A. Kino and R. E. Vesley, North-Holland Publ. Co., Amsterdam (1970), 53–71.

    Google Scholar 

  5. D. S. Bridges, Constructive Functional Analysis, Pitman, London (1979).

    MATH  Google Scholar 

  6. S. Feferman, Theories of finite type related to mathematical logic, edited by J. Barwise, Studies in Logic and the Foundations of Mathematics 90 North-Holland Publ. Co., Amsterdam (1977).

    Google Scholar 

  7. H. Friedman, Set theoretic foundations for constructive analysis, Ann. Math. (2) 105 (1977), 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Goodman—J. Myhill, The formalization of Bishop's constructive mathematics, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics 274, Springer-Verlag, Berlin (1972), 83–96.

    Book  Google Scholar 

  9. H. Hahn, Über lineare Gleichungssysteme in lineare Räumen, J. reine und angew. Math. 157 (1927), 214–229.

    MATH  Google Scholar 

  10. G. Kreisel, Analysis of the Cantor-Bendixson theorem by means of the analytic hierarchy, Bulletin of the Polish Acad. Sci. 7 (1959), 371–391.

    MathSciNet  MATH  Google Scholar 

  11. G. Kreisel, The axiom of choice and the class of hyperarithmetic functions, Dutch Acad. A, 65 (1962), 307–319.

    MathSciNet  MATH  Google Scholar 

  12. W. Rudin, Real and Comolex Analysis, McGraw-Hill Book Co., N.Y. (1966).

    Google Scholar 

  13. G. Takeuti, Proof Theory, North-Holland Publ. Co., Amsterdam (1975).

    MATH  Google Scholar 

  14. G. Takeuti, Two Applications of Logic to Mathematics, Iwanami Shoten Publ. Co. and Princeton Univ. Press, Tokyo (1978).

    MATH  Google Scholar 

  15. M. Yasugi, Arithmetically definable analysis, Proceedings of Research Institute of Mathematical Science, Kyoto University 180 (1973), 39–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gert H. Müller Gaisi Takeuti Tosiyuki Tugué

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Yasugi, M. (1981). The Hahn-Banach theorem and a restricted inductive definition. In: Müller, G.H., Takeuti, G., Tugué, T. (eds) Logic Symposia Hakone 1979, 1980. Lecture Notes in Mathematics, vol 891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090989

Download citation

  • DOI: https://doi.org/10.1007/BFb0090989

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11161-0

  • Online ISBN: 978-3-540-38633-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics