A note on Majkić's systems (Q609767)

The authors of this note prove that \textit{Z. Majkić}'s \(Z_n\) and \(CZ_n\) [Notre Dame J. Formal Logic 49, No. 4, 401--424 (2008; Zbl 1180.03030)], which are variations of \textit{N. C. A. da Costa}'s hierarchy \(C_n\), cf. [Notre Dame J. Formal Logic 15, 497--510 (1974; Zbl 0236.02022)], are not hierarchies of paraconsistent logic. By giving a simple axiomatization of \(Z_n\) and \(CZ_n\) that is different from the original one, they prove that they are not actually hierarchies and that, as they are in fact extensions of intuitionistic propositional calculus, they are not paraconsistent systems.