Skip to main content
Log in

What does logic have to tell us about mathematical proofs?

  • Report and dialogue
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. J. Ax, S. Kochen, Diophantine problems over local fields, I, II,Amer. J. Math. 87 (1965), 605–630

    Article  MathSciNet  Google Scholar 

  2. J. Barwise (ed.),Handbook of Mathematical Logic, North-Holland, Amsterdam 1977

    Google Scholar 

  3. J. Barwise, J. Schlipf, An introduction to recursively saturated and resplendent models,J. Symbolic Logic 41 (1976), 531–536

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. P.J. Cohen, Decision procedures for real and p-adic fields,Comm. Pure Appl. Math. 22 (1969), 131–151

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Davis, Y. Matijasevič, J. Robinson, Hilbert’s 10th problem. Diophantine equations: positive aspects of a negative solution,Proc. Symp. Pure Math. 28, Amer. Math. Soc., 1976

  8. N.G. de Bruijn, The mathematical language AUTOMATH, its usage and some of its extensions,Lecture Notes in Mathematics 125, Springer, Berlin 1970, 29–61

    Google Scholar 

  9. S. Feferman, A language and axioms for explicit mathematics,Lecture Notes in Mathematics 450, Springer, Berlin 1975, 87–139

    Google Scholar 

  10. S. Feferman,Theories of finite type related to mathematical practice, in [2], 913–971

  11. H. Friedman, Set theoretic foundations of constructive analysis,Ann of Math. 109 (1977), 1–28

    Article  Google Scholar 

  12. G. Gentzen,The Collected Papers of Gerhard Gentzen (ed. by M. Szabo), North-Holland, Amsterdam 1969

    Google Scholar 

  13. G. Kreisel, Mathematical significance of consistency proofs,J. Symbolic Logic 23 (1958), 155–182

    Article  MathSciNet  Google Scholar 

  14. G. Kreisel, What have we learnt from Hubert’s second problem?Proc. Symp. Pure Math. 28 (1976), 93–130

    MathSciNet  Google Scholar 

  15. Y.I. Manin,Course in Mathematical Logic, Springer, Berlin 1977

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Prawitz,Natural Deduction: A Proof-theoretical Study, Almquist and Wiksell, Stockholm 1965

  18. D. Prawitz,Ideas and results in proof theory, Proc. Second Scandinavian Logic Symp., North-Holland, Amsterdam 1971, 235–307

    Chapter  Google Scholar 

  19. K. Schütte,Proof Theory, Springer, Berlin 1978. (Review to appear inBull. Amer. Math. Soc.)

    Google Scholar 

  20. R. Smullyan,Theory of Formal Systems, Princeton University Press, Princeton 1961

    MATH  Google Scholar 

  21. G. Takeuti,Proof Theory, North-Holland, Amsterdam 1975. (Reviewed inBull. Amer. Math. Soc. 83 (1977), 351-361)

    Google Scholar 

  22. W.T. Tutte, Colouring problems,The Mathematical Intelligencer 1 (1978), 72–75

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feferman, S., Feferman, S. What does logic have to tell us about mathematical proofs?. The Mathematical Intelligencer 2, 20–24 (1979). https://doi.org/10.1007/BF03024381

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024381

Keywords

Navigation