Skip to main content
SpringerLink
Log in

Undecidability, incompleteness and Arnol'd problems

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, T. Lindstrom,Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press (1986).

  2. V. I. Arnol'd, ‘Problems of Present Day Mathematics,’ XVII (Dynamical systems and differential equations),Proc. Symp. Pure Math. 28, 59 (1976).

    Google Scholar 

  3. V. I. Arnol'd, e-mail message to FAD (1992).

  4. J. Casti,Reality rules, II, p. 350–351, John Wiley (1992).

  5. B. F. Caviness,J. of the ACM 17, 385 (1970).

    Google Scholar 

  6. N. C. A. da Costa andF. A. Doria,Int. J. Theor. Phys. 30, 1041 (1991).

    Google Scholar 

  7. N. C. A. da Costa and F. A. Doria, ‘On Arnol'd's Hilbert Symposium Problems,’ in G. Gottlob, A. Leitsch, D. Mundici, eds.,Proceedings of the 1993 Kurt Gödel Colloquium: Computational Logic and Proof Theory, Lecture Notes in Computer Science713, Springer (1993), pp. 152–158.

  8. N. C. A. da Costa andF. A. Doria,Int. J. Theor. Phys. 33, 1913 (1994).

    Google Scholar 

  9. N. C. A. da Costa and F. A. Doria, ‘Gödel Incompleteness, Explicit Expressions for Complete Degrees and Applications,’ to appear inComplexity 1 (1995).

  10. N. C. A. da Costa, F. A. Doria andA. F. Furtado-do-Amaral, ‘A Dynamical System where Proving Chaos is Equivalent to Proving Fermat's Conjecture,’Int. J. Theor. Phys. 32, 2187–2206 (1993).

    Google Scholar 

  11. N. C. A. da Costa, F. A. Doria, J. A. Baêta Segundo, D. Krause, ‘On Arnol'd's 1974 Hilbert Symposium Problems,’ to appear (1993).

  12. M. Davis, ‘Hilbert's Tenth Problem is Unsolvable,’ inComputability and Unsolvability, 2nd. edition, Dover (1982).

  13. F. A. Doria, in J. Casti and J. Traub,On limits, preprint 94-10-056, Santa Fe Institute (1994).

  14. E. Hopf,Sachsische Akad. der Wiss.,Math.-Phys. Serie 94, 1 (1942).

    Google Scholar 

  15. J. E. Marsden, M. McCracken,The Hopf Bifurcation and its Applications, Springer (1976).

  16. D. Miller,Critical rationalism, Open Court, Chicago (1994).

    Google Scholar 

  17. D. Richardson,J. Symbol. Logic 33, 514 (1968).

    Google Scholar 

  18. I. Stewart,Nature 352, 664 (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Group on Logic and Foundations Institute for Advanced Studies, University of São Paulo, Av. L. Gualberto, Trav. J, 374, 05655-010, São Paulo SP, Brazil

    Newton C. A. da Costa

  2. Research Center on Math. Theories of Communication School of Communications, Fed. Univ. at Rio de Janeiro, Av. Pasteur, 250, 22295-900, Rio RJ, Brazil

    Francisco A. Doria

Authors
  1. Newton C. A. da Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francisco A. Doria
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by FAPESP and CNPq (Brazil, Philosophy Section).

Rights and permissions

Reprints and permissions

About this article

Cite this article

da Costa, N.C.A., Doria, F.A. Undecidability, incompleteness and Arnol'd problems. Stud Logica 55, 23–32 (1995). https://doi.org/10.1007/BF01053030

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01053030

Keywords

Search

Navigation