Disjoint sets $A,B\subseteq\mathbb N$ are <recursively inseparable sets>[recursively inseparable] when there is no recursive $C\subseteq\mathbb N$ such that
$$
A\subseteq C,
\qquad
B\cap C=\varnothing.
$$

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 120 / 2 / e / Solution

{wiki=Recursive_set#Computably_inseparable_sets}

Disjoint sets $A,B\subseteq\mathbb N$ are recursively inseparable when no recursive set $C$ satisfies $A\subseteq C$ and $B\cap C=\varnothing$.


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 Incoming links: Recursively inseparable sets