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.
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References
S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, T. Lindstrom,Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press (1986).
V. I. Arnol'd, ‘Problems of Present Day Mathematics,’ XVII (Dynamical systems and differential equations),Proc. Symp. Pure Math. 28, 59 (1976).
V. I. Arnol'd, e-mail message to FAD (1992).
J. Casti,Reality rules, II, p. 350–351, John Wiley (1992).
B. F. Caviness,J. of the ACM 17, 385 (1970).
N. C. A. da Costa andF. A. Doria,Int. J. Theor. Phys. 30, 1041 (1991).
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.
N. C. A. da Costa andF. A. Doria,Int. J. Theor. Phys. 33, 1913 (1994).
N. C. A. da Costa and F. A. Doria, ‘Gödel Incompleteness, Explicit Expressions for Complete Degrees and Applications,’ to appear inComplexity 1 (1995).
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).
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).
M. Davis, ‘Hilbert's Tenth Problem is Unsolvable,’ inComputability and Unsolvability, 2nd. edition, Dover (1982).
F. A. Doria, in J. Casti and J. Traub,On limits, preprint 94-10-056, Santa Fe Institute (1994).
E. Hopf,Sachsische Akad. der Wiss.,Math.-Phys. Serie 94, 1 (1942).
J. E. Marsden, M. McCracken,The Hopf Bifurcation and its Applications, Springer (1976).
D. Miller,Critical rationalism, Open Court, Chicago (1994).
D. Richardson,J. Symbol. Logic 33, 514 (1968).
I. Stewart,Nature 352, 664 (1991).
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Partially supported by FAPESP and CNPq (Brazil, Philosophy Section).
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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
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DOI: https://doi.org/10.1007/BF01053030