A Beautiful Theorem
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.
KeywordsMaymin’s theorem Efficient markets O’Donnell’s algorithm Almost efficient markets
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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