Advertisement

The Π11-comprehension schema and ω-rules

  • Gaisi Takeuti
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 70)

Keywords

Function Symbol Recursive Function Mathematical Induction Logical Inference Ordinal Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    G. Gentzen, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Math. Ann., 119 (1943), 140–161.MathSciNetCrossRefzbMATHGoogle Scholar
  2. (2).
    A. Kino, On provably recursive functions and ordinal recursive functions, to appear in J. Math. Soc. Japan.Google Scholar
  3. (3).
    G. Kreisel, Mathematical Logic, Lectures on Modern Mathematics, vol. III, 95–195, New York, 1965.MathSciNetzbMATHGoogle Scholar
  4. (4).
    K. Schütte, Beweistheorie, Springer, 1960.Google Scholar
  5. (5).
    G. Takeuti, A remark on Gentzen's paper ‘Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie', I, II, Proc. Japan Acad., 39 (1963), 263–269.MathSciNetCrossRefzbMATHGoogle Scholar
  6. (6).
    G. Takeuti, Consistency proofs of subsystems of classical analysis, Ann. of Math., 86 (1967), 299–348.MathSciNetCrossRefzbMATHGoogle Scholar
  7. (7).
    G. Takeuti and M. Yasugi, Reflection principles of subsystems of analysis, to appear.Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Gaisi Takeuti

There are no affiliations available

Personalised recommendations