Finite structural axiomatization of every finite-valued propositional calculus

In [2] A. Wroski proved that there is a strongly finite consequence C which is not finitely based i.e. for every consequence C⁺ determined by a finite set of standard rules C C⁺. In this paper it will be proved that for every strongly finite consequence C there is a consequence C⁺ determined by a finite set of structural rules such that C(Ø)=C⁺(Ø) and = (where , are consequences obtained by adding to the rules of C, C⁺ respectively the rule of substitution). Moreover it will be shown that under certain assumptions C=C⁺.