Contradiction from the Fixed Point Lemma

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Assuming that PRA (primitive recursive arithmetic) is consistent and Church's Thesis is true, the Fixed Point Lemma enables the derivation of a contradiction, in a manner akin to the v-Curry paradox. The derivation could be blocked by excluding certain formulae from the scope of the Lemma, but this would effectively concede that the unrestricted Lemma is false. The resolution of the paradox thus remains an open question.
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First archival date: 2021-02-19
Latest version: 10 (2021-03-15)
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