 Then \(\vdash\) provides da Costa’s system \(C_1\). If we let \(A^1\) abbreviate the formula \(\neg(A \wedge \neg A)\) and \(A^{n+1}\) the formula \((\neg(A^n \wedge \neg A^n ))^1\), then we obtain \(C_i\) for each natural number \(i\) greater than 1.