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$\overline{K}\;\leq\;\{ \langle p,q\rangle \mid \mathtt{Dom}(\varphi_p)\subset\mathtt{Dom}(\varphi_q)\subset\mathtt{Im}(\varphi_p) \}$
Reduce $\overline{K}$ to the set of pairs of natural numbers codifying programs
such that the domain of the function computed by the machine codified by the
first one is strictly included into the domain of the function computed by the
machine codified by the second one, which in turn is strictly included into the
image of the function computed by the machine codified by the first one
(roughly, the set of pairs of programs such that the domain of the function
computed by the first one is strictly included into the domain of the function
computed by the second one, which in turn is strictly included into the image
of the function computed by the first one), in order to prove that such set is
not semi-decidable (not recursively enumerable).
Authors: Carles Creus, Guillem Godoy
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