Skip to main content
SpringerLink
Log in

Notes on intuitionistic second order arithmetic

  • Intuitionism
  • Conference paper
  • First Online:
Cambridge Summer School in Mathematical Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 337))

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
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

  • H. Friedman A Some applications of Kleene's methods for intuitionistic systems. This volume.

    Google Scholar 

  • G. Gentzen 1933, Ãœber das Verhältnis zwischen intuitionistischer und klassischer Arithmetik. First published in English translation in: M.E. Szabo (editor), The collected papers of Gerhard Gentzen, Amsterdam-London (North-Holland), 1969, pp. 53–67.

    Google Scholar 

  • J.Y. Girard 1971 Une extension de l'interprétation de Gödel à l'analyse et son application à l'élimination des coupures dans l'analyse et la théorie des types, in: J.E. Fenstad (editor), Proceedings of the second Scandinavian Logic Symposium, Amsterdam — London (North-Holland).

    Google Scholar 

  • A Quelques résultats sur les interprétations fonctionnelles. Lecture Notes in Mathematics, vol. 337 (this volume).

    Google Scholar 

  • K. Gödel 1958 Ãœber eine bisher noch nicht benutzte Erweiterung des finiten Standpunktes. Dialectica 12 (1958), pp. 280–287.

    Article  MathSciNet  MATH  Google Scholar 

  • H.R. Jerwell 1971 A normal form in first order arithmetic, in: J.E. Fenstad (editor), Proceedings of the second Standinavian Logic Symposium, Amsterdam — London (North-Holland).

    Google Scholar 

  • S.C. Kleene 1945 On the interpretation of intuitionistic number theory. J. Symb. Logic 10 (1945), pp. 109–124.

    Article  MathSciNet  MATH  Google Scholar 

  • 1952 Introduction to metamathematics. Amsterdam, Groningen (North-Holland, Noordhoff) and New York (Van Nostrand).

    MATH  Google Scholar 

  • 1962 Disjunction and existence under implication in elementary intuitionistic formalisms. J. Symb. Logic 27 (1962), pp. 11–18.

    Article  MathSciNet  MATH  Google Scholar 

  • S. C. Kleene and R. E. Vesley 1965 Foundations of intuitionistic mathematics, especially in relation to recursive function. Amsterdam (North-Holland).

    Google Scholar 

  • G. Kreisel 1959 Reflection principle for subsystems of Heyting's arithmetic (abstract). J. Symb. Logic 24 (1959), p. 322.

    Google Scholar 

  • 1968 Functions, ordinals, species, in: J.F. Staal, and B. van Rootselaar (editors), Logic, Methodology and Philosophy of Sciences III, Amsterdam (North-Holland).

    Google Scholar 

  • 1970 Church's thesis: a kind of reducibility axiom for constructive mathematics, in: A. Kino, J. Myhill, R.E. Vesley (editors), Intuitionism and Proof Theory, Amsterdam (North-Holland).

    Google Scholar 

  • 1971 A survey of proof theory II, in: J.E. Fenstad (editor), Proceedings of the second Scandinavian Logic Symposium, Amsterdam — London (North-Holland).

    Google Scholar 

  • G. Kreisel and A.S. Troelstra 1970 Formal systems for some branches of intuitionistic analysis, Annals of Mathematical Logic 1 (1970), pp. 229–387.

    Article  MathSciNet  MATH  Google Scholar 

  • D. Prawitz 1965 Natural deduction, a proof-theoretical study, Stockholm, Göteborg, Uppsala (Almqvist and Wiksell).

    Google Scholar 

  • 1970 Some results for intuitionistic logic with second order quantification rules, in: A. Kino, J. Myhill, R.E. Vesley (editors), Intuitionism and Proof Theory, Amsterdam (North-Holland).

    Google Scholar 

  • 1971 Ideas and results in proof theory, in: J.E. Fenstad (editor), Proceedings of the second Scandinavian Logic Symposium, Amsterdam — London (North-Holland).

    Google Scholar 

  • A Towards a foundation of general proof theory. To appear in: Logic, Methodology and Philosophy of Science IV.

    Google Scholar 

  • B. Scarpellini 1970 On cut elimination in intuitionistic systems of analysis, in: A. Kino, J. Myhill, R.E. Vesley (editors), Intuitionism and Proof Theory, Amsterdam (North-Holland).

    Google Scholar 

  • 1971 Proof theory and intuitionistic systems. Berlin, Heidelberg, New York (Springer-Verlag).

    Google Scholar 

  • A. S. Troelstra 1971 Notions of realizability for intuitionistic arithmetic and intuitionistic arithmetic in all finite types, in: J.E. Fenstad (editor), Proceedings of the second Scandinavian Logic Symposium, Amsterdam, London (North-Holland).

    Google Scholar 

  • 1971 A Computability of terms and notions of realizability for intuitionistic analysis. Report 71-02 of the Department of Mathematics, University of Amsterdam (mimeographed).

    Google Scholar 

Download references

Authors
  1. A. S. Troelstra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. R. D. Mathias H. Rogers

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Troelstra, A.S. (1973). Notes on intuitionistic second order arithmetic. In: Mathias, A.R.D., Rogers, H. (eds) Cambridge Summer School in Mathematical Logic. Lecture Notes in Mathematics, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066774

Download citation

  • DOI: https://doi.org/10.1007/BFb0066774

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05569-3

  • Online ISBN: 978-3-540-36884-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation