 Let \(C = \{\Sigma_i : i \in I\}\) and \(\varrho\) a permeability relation on \(C\) such that \(\varrho\) is a map from \(I \times I\) to subsets of formulas of the language. If \(i_0 \in I\), then any structure \(\langle C, \varrho , i_0\rangle\) is called a C&amp;P structure on \(\Sigma\). If \(\mathcal{B}\) is a C&amp;P structure on \(\Sigma\), we define the C&amp;P consequences of \(\Sigma\) with respect to \(\mathcal{B}\), as follows. For each \(i \in I\), a set of sentences, \(\Sigma_i^n\), is defined by recursion on \(n\):