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”).

A tough construction to translate literally, especially as it is used on page 86. We opt. for “apply this directly”.

Throughout section 3 text is a little confused (or confusing) about what system exactly it wishes to call “propositional calculus”. Different calculi presented throughout section 3 are potential references for the term “propositional calculus”. A single meaning does seem to have been achieved by the end of section 3 (on p 82).