Since the Hilbert substitution method has been applied by Ackermann to the formalism Z of number theory in [3], we shall give the no-counter-example interpretation for extensions (c) of Z, e.g. Zμ. The work required on top of Ackermann's investigations to check conditions (α) and (β), consists only in a suitable definition of a class of recursive functional. The verification of (γ) and (δ) is much more difficult, and requires the ideas of paras. 32 and 33 in the preceding section.