Translated as “genus” following its almost specific definition as something constructive (as in Brouwer’s and later intuitionistic use of “species”), or something resulting from a “genetic” method on page 1-2.

However Hilbert and Bernays seem to use “gattung” inconsistently, especially on p. 88 where it seems to mean simply “sort” (possibly on p.41 as well, where it could also mean “set”).