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$\overline{K}\;\leq\;\{ \langle p,q\rangle \mid |\mathtt{Dom}(\varphi_p)|=\infty\;\wedge\;|\mathtt{Dom}(\varphi_q)|=\infty\;\wedge\;\mathtt{Dom}(\varphi_p)\cap\mathtt{Dom}(\varphi_q)=\emptyset \}$
Reduce $\overline{K}$ to the set of pairs of natural numbers codifying programs
such that the domains of the functions implemented by them are infinite and
share no element (roughly, the set of pairs of programs implementing functions
whose domains are infinite and share no element), in order to prove that such
set is not semi-decidable (not recursively enumerable).
Authors: Carles Creus, Guillem Godoy
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