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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 Thcorcms 9 and 10 wediscuss the complexity of the set of founded elements in a recursively enumerable relation on the set JJ of natural numbers, in the framework of reduction between relations. We alsofind an application in the theory of diagonahzable algebras and construct an undecidable formula

Translating the hypergame paradox: Remarks on the set of founded elements of a relation