Rice’s Theorem is a notorious stumbling block in Computer Science. We review some previous work of us that shows that we can extend Rice’s result to large segments of everyday mathematics, so that similar stumbling blocks appear in many areas of mathematics, as well as applied areas such as mathematical economics; one of its applications (Koppl’s conjecture) is discussed in some detail. Note: this paper has been written in an informal style.
The authors are members of the Brazilian Academy of Philosophy. F. A. Doria wishes to thank R. Koppl who kindly invited him to present these ideas at the Wirth meeting; the authors also thank Koppl for many comments on his conjecture. The authors also thank an anonymous referee for many detailed criticisms that greatly improved the present paper. This paper was supported in part by CNPq, Philosophy Section. 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. Finally, the authors thank Profs. R. Bartholo, C. A. Cosenza, S. Fuks (in memoriam), S. Jurkiewicz, R. Kubrusly, and F. Zamberlan for support.
da Costa, N.C.A. and Doria, F.A. (2014), "On an Extension of Rice’s Theorem and its Applications in Mathematical Economics Dedicated to the memory of Professor Saul Fuks (1929–2012).
Dedicated to the memory of Professor Saul Fuks (1929–2012).
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