Skip to main content
SpringerLink
Log in

The formalization of Bishop's constructive mathematics

  • Conference paper
  • First Online:
Toposes, Algebraic Geometry and Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 274))

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
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. M. J. Beeson, Metamathematics of constructive analysis, Ph.D. Thesis, Stanford University, 1971.

    Google Scholar 

  2. E. Bishop, Foundations of Constructive Analysis (McGraw-Hill, New York, 1967).

    MATH  Google Scholar 

  3. E. Bishop, Mathematics as a numerical language, in: Intuitionism and Proof Theory, ed. J. Myhill, A. Kino, and R. E. Vesley (North-Holland, Amsterdam, 1970) 53–71.

    Google Scholar 

  4. K. Gödel, On intuitionistic arithmetic and number theory, trans. M. Davis, in: The Undecidable, ed. M. Davis (Raven Press, Hewlett, N.Y., 1965) 75–81.

    Google Scholar 

  5. N. D. Goodman, Intuitionistic arithmetic as a theory of constructions, Ph.D. Thesis, Stanford University, 1968.

    Google Scholar 

  6. N. D. Goodman, The theory of the Gödel functionals, In preparation.

    Google Scholar 

  7. G. Kreisel, Hilbert's programme, in: Philosophy of Mathematics, ed. P. Benaceraff and H. Putnam (Prentice-Hall, Englewood Cliffs, N.J., 1964) 157–180.

    Google Scholar 

  8. G. Kreisel, Informal rigour and completeness proofs, in: Problems in the Philosophy of Mathematics, ed. I. Lakatos (North-Holland, Amsterdam, 1967) 138–171.

    Chapter  Google Scholar 

  9. J. Myhill, Embedding classical type theory in ‘intuitionistic’ type theory, in: Axiomatic Set Theory, ed. D. S. Scott (Proc. Symp. Pure Math. 13, Part I, 1971) 267–270.

    Google Scholar 

  10. W. W. Tait, Intensional interpretation of functionals of finite type I, J. Symb. Log. 32 (1967) 198–212.

    Article  MATH  MathSciNet  Google Scholar 

  11. W. W. Tait, Constructive reasoning, in: Logic, Methodology and Philosophy of Science III, ed. B. van Rootselaar and J. F. Staal (North-Holland, Amsterdam, 1968) 185–199.

    Chapter  Google Scholar 

  12. A. S. Troelstra, The theory of choice sequences, in: Logic Methodology and Philosophy of Science III, ed. B. van Rootselaar and J. F. Staal (North-Holland, Amsterdam, 1968) 201–223.

    Chapter  Google Scholar 

  13. A. S. Troelstra, Notions of realizability for intuitionistic arithmetic and intuitionistic arithmetic in all finite types. To appear.

    Google Scholar 

  14. M. Yasugi, Intuitionistic analysis and Gödel's interpretation, J. Math. Soc. Japan, 15 (1963) 101–112.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State University of New York at Buffalo, USA

    Nicolas D. Goodman & John Myhill

Authors
  1. Nicolas D. Goodman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John Myhill
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

F. W. Lawvere

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Goodman, N.D., Myhill, J. (1972). The formalization of Bishop's constructive mathematics. In: Lawvere, F.W. (eds) Toposes, Algebraic Geometry and Logic. Lecture Notes in Mathematics, vol 274. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073966

Download citation

  • DOI: https://doi.org/10.1007/BFb0073966

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05920-2

  • Online ISBN: 978-3-540-37609-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation