Translating the hypergame paradox: Remarks on the set of founded elements of a relation |
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| Authors: | Claudio Bernardi Giovanna D'Agostino |
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| Institution: | (1) Department of Mathematics, University  La Sapienza , Rome, Italy;(2) Department of Mathematics and Computer Science, University of Udine, Italy |
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| Abstract: | In Zwicker (1987) the hypergame paradox is introduced and studied. In this paper we continue this investigation, comparing the hypergame argument with the diagonal one, in order to find a proof schema. In particular, in Theorems 9 and 10 we discuss the complexity of the set of founded elements in a recursively enumerable relation on the set N of natural numbers, in the framework of reduction between relations. We also find an application in the theory of diagonalizable algebras and construct an undecidable formula. |
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