 At the end of his letter, Bernays mentions that Herbrand misunderstood him in a recent conversation on which Herbrand had reported in a letter to Gödel with a copy to Bernays. Not only had Herbrand misunderstood Bernays, but Bernays had also misunderstood Herbrand as to the extent of the latter’s consistency result that was to be published a few months later as Herbrand 1931. Bernays understood Herbrand as having claimed that he had established the consistency of full first-order arithmetic: Herbrand’s system is indeed a first-order theory with a rich collection of finitist functions, but it uses the induction principle only for quantifier-free  formulae.[7]  Gödel asserted in December 1933 that this theorem of Herbrand’s was even then the strongest result that had been obtained in the pursuit of Hilbert’s finitist program, and he formulated the result in a beautiful informal way as follows: