Abstract
We first present Maymin’s Theorem on the existence of efficient markets; it is a result that connects mathematical economics and computer science. We then introduce O’Donnell’s algorithm for the solution of NP-complete problems and the concept of almost efficient markets; we state the main result, which is: given a metamathematical condition, there will be almost efficient markets. We then briefly discuss whether changing the underlying logical framework we would be able to change the preceding results.
Dedicated to Jair Minoro Abe for his 60th birthday
A thing of beauty is a joy for ever:
Its loveliness increases; it will never
Pass into nothingness
John Keats, Endymion
Partially supported by CNPq, Philosophy Section; the first author is a member of the Brazilian Academy of Philosophy.
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Notes
- 1.
Actually we know very little.
- 2.
Actually we deal with a slightly larger class of Boolean expressions.
- 3.
Conjunctive normal form.
- 4.
The BGS machine set is a set of time-polynomial Turing machines which includes algorithms that mimic all time-polynomial Turing machines. See above and check [1].
References
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Maymin, P.Z.: Markets are efficient if and only If \(P=NP\). Algorithmic Finance, 1(1), 1 (2011)
O’Donnell, M.: A programming language theorem which is independent of Peano arithmetic. In: Proceedings of 11th Annual ACM Symposium on the Theory of Computation, pp. 176–188 (1979)
Post, E.L.: Introduction to a general theory of elementary propositions. Am. J. Math. 43, 163 (1921)
Acknowledgments
This paper was supported in part by CNPq, Philosophy Section Grant no. 4339819902073398. It is part of the research efforts of the Advanced Studies Group, Production Engineering Program, at Coppe–UFRJ and of the Logic Group, HCTE–UFRJ. We thank Profs. R. Bartholo, S. Fuks (in memoriam), S. Jurkiewicz, R. Kubrusly, and F. Zamberlan for support.
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Doria, F.A., Cosenza, C.A. (2016). A Beautiful Theorem. In: Akama, S. (eds) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-40418-9_10
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DOI: https://doi.org/10.1007/978-3-319-40418-9_10
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