Skip to main content

Formalizing constructive mathematics: Why and how?

  • Conference paper
  • First Online:
Constructive Mathematics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 873))

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. Beeson, M. J.: Principles of continuous choice and continuity of functions in formal systems for constructive mathematics. Annals of Math. Logic, 12, 249–322 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  2. Beeson, M. J.: Continuity in intuitionistic set theories. In Logic Colloquium '78 (ed. Boffa, M., van Dalen, D., and MacAloon, K.). Amsterdam: North-Holland 1979.

    Google Scholar 

  3. Beeson, M. J.: A theory of constructions and proofs. To appear in J. Symbolic Logic. Preprint version: University of Utrecht, preprint no. 134, Nov. 1979.

    Google Scholar 

  4. Beeson, M. J.: Problematic principles in constructive mathematics. To appear in Logic Colloquium '80, or elsewhere if this volume is not published.

    Google Scholar 

  5. Beeson, M. J.: Recursive models for constructive set theory. To appear. (Submitted to Annals of Math. Logic). Preprint version: University of Utrecht, preprint no. 179, Nov. 1980.

    Google Scholar 

  6. Bishop, E.: Foundations of Constructive Analysis. New York: McGraw-Hill 1967.

    MATH  Google Scholar 

  7. Bishop, E., and Cheng, H.: Constructive measure theory. Memoirs of the AMS 116. Providence, R. I. (1972).

    Google Scholar 

  8. Bridges, D.: Constructive Functional Analysis. London: Pitman 1979.

    MATH  Google Scholar 

  9. Feferman, S.: A language and axioms for explicity mathematics. In Algebra and Logic, Springer Lecture Notes No. 450. Berlin-Heidelberg-New York: Springer 1975.

    Chapter  Google Scholar 

  10. Feferman, S.: Constructive theories of functions and classes. In Logic Colloquium '78 (ed. Boffa, M., van Dalen, D., and MacAloon, K.) Amsterdam: North-Holland 1979.

    Google Scholar 

  11. Friedman, H.: Set-theoretic foundations for constructive analysis. Annals of Math. 105, 1–28 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  12. Greenleaf, N.: Liberal constructive set theory. This volume.

    Google Scholar 

  13. Kleene, S., and Vesley, R.: The Foundations of Intuitionistic Mathematics, Especially in Relation to Recursive Function Theory. Amsterdam: North-Holland 1965.

    Google Scholar 

  14. Kreisel, G.: Mathematical logic. In Lectures on Modern Mathematics (ed. Saaty, T.). New York: Wiley 1965.

    Google Scholar 

  15. Martin-Löf, P.: An intuitionistic theory of types: predicative part. In Logic Colloquium '73 (ed. Rose, H.E., and Shepherdson, J.C.). Amsterdam: North-Holland 1975.

    Google Scholar 

  16. Martin-Löf, P.: Constructive mathematics and computer programming. Preprint No. 11, University of Stockholm, 1979.

    Google Scholar 

  17. Myhill, J.: Constructive set theory. J. Symbolic Logic 40, 347–383 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  18. Smullyan, R.: Theory of Formal Systems. Princeton: Princeton University Press 1961, rev. 1963.

    Google Scholar 

  19. Troelstra, A.S.: Principles of Intuitionism. Springer Lecture Notes No. 95. Berlin-Heidelberg-New York: Springer 1969.

    MATH  Google Scholar 

  20. Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Springer Lecture Notes No. 344. Berlin-Heidelberg-New York: Springer 1973.

    MATH  Google Scholar 

  21. Troelstra, A.S.: Constructive mathematics. In Handbook of Mathematical Logic (ed. Barwise, J.). Amsterdam: North-Holland 1977.

    Google Scholar 

  22. Troelstra, A.S.: A note on non-extensional operations in connection with continuity and recursiveness. Indagationes Math. 39, 455–462 (1977).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Fred Richman

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Beeson, M.J. (1981). Formalizing constructive mathematics: Why and how?. In: Richman, F. (eds) Constructive Mathematics. Lecture Notes in Mathematics, vol 873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090733

Download citation

  • DOI: https://doi.org/10.1007/BFb0090733

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10850-4

  • Online ISBN: 978-3-540-38759-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics