 To obtain da Costa’s system \(C_{\omega}\), instead of the positive fragment of classical logic, we start with positive intuitionist logic instead. \(C_i\) systems for finite \(i\) do not rule out \((A^n \wedge \neg A^n \wedge A^{n+1})\) from holding in a theory. By going up the hierarchy to \(\omega\), \(C_{\omega}\) rules out this possibility. Note, however, that \(C_{\omega}\) is not a LFC as it does not contain classical positive logic. For the semantics for da Costa’s \(C\)-systems, see for example da Costa and Alves 1977 and Loparic 1977.