 for some detachable subset \(D\) of \(2^*\). Every detachable subset of \(2^*\) is a \(\mathsf{c}\)-subset. On the other hand, by a \(\Pi^{0}_1\)-subset of \(2^*\) we mean a subset \(B\) of \(2^*\) with the following property: there exists a detachable subset \(S\) of \(2^* \times \bN\) such that