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Yes coRE is closed under concatenation: Let $L_1, L_2$ be coRE, witnessed by Turing Machines $M_1,M_2$ whose domain is the complement of $L_1,L_2$ respectively. We then build a Turing Machine $M$ whose domain is the complement of $L_1\cdot L_2$: on input $u$, $M$ will enumerate the finitely many ways to decompose $u$ into $u_1u_2$, and for each of them run $...


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