 The alternative interpretation argues that Frege’s understanding of consistency and independence is sufficiently different from Hilbert’s that the entailment in question does not hold: that the satisfiability of \(R_{\textit{AX}}\), and the consequent consistency in Hilbert’s sense of AX, does not entail the consistency in Frege’s sense of \(\textit{AX}_{G}\). Similarly for independence. According to this interpretation, Frege is right to claim that Hilbert’s demonstrations fail to show consistency and independence in the sense in which he, Frege, understands these  terms.[9]