Semidecidable least-representative transversal
= Semidecidable least-representative transversal
{title2=$S=\{n:\forall m<n\ (m\not\sim n)\}$}
For a <co-computably enumerable equivalence relation>, the least element of each <equivalence class> forms a complete <transversal of a set family>. Membership is <semidecidable>: run the finitely many inequivalence tests against smaller numbers in parallel and accept when all succeed. Infinitely many classes are needed only to make the resulting transversal infinite.