Abstract
We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is computable.
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References
Buser, P. (1972), Darstellung von Prädikaten durch analytische Funktionen, Diplomarbeit, Universität Basel, pp. 1–41.
da Costa, A. and Doria, A. (1991a), Undecidability and Incompleteness in Classical Mechanics, Int. J. Theoret. Phys. 30(8), pp. 1041–1073.
da Costa, A. and Doria, A. (1991b), Classical Physics and Penroses Thesis, Found. of Phys. Letters 4(4), pp. 343–373.
Davis, M. (1958), Computability and Unsolvability, New York: McGraw-Hill.
Hancock, H. (1958), Theory of Elliptic Functions, Dover Publishing.
Matijasevich, J. (1970), 'Enumerable Sets are Diophantine', Soviet Math. Doklady 11, pp. 354–357.
Penrose, R. (1989), The Emperors New Mind, Oxford: Oxford University Press.
Pour-El, M. and Richards, I. (1981), 'The Wave Equation with Computable Initial Data Such That Its Unique Solution Is Not Computable', Advances in Math. 39, pp. 215–239.
Smullyan, R. (1961), Theory of Formal Systems, Princeton, NJ: Princeton University Press.
Golubitsky, M. and Schaeffer, D. (1985), Singularities and Groups in Bifurcation Theory, NewYork: Springer.
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Scarpellini, B. Comments on `Two Undecidable Problems of Analysis'. Minds and Machines 13, 79–85 (2003). https://doi.org/10.1023/A:1021364916624
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DOI: https://doi.org/10.1023/A:1021364916624