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$\overline{K}\;\leq\;\{ p \mid |\mathtt{Im}(\varphi_p)|=2 \}$
Reduce $\overline{K}$ to the set of natural numbers codifying programs such
that the image of the function computed by the program has cardinal $2$
(roughly, the set of programs implementing functions whose image has exactly
two elements) in order to prove that such set is not semi-decidable (not
recursively enumerable).
Authors: Carles Creus, Guillem Godoy
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