 Frege also does not construct the general theory of the arithmetic of cardinal and ordinal numbers that occupies PM for much of Part III. Indeed, after the theorems on Arithmetic in §54 which concludes Part II of Basic Laws of Arithmetic, Frege jumps directly to the topic of Real Numbers for the remainder of Volume II. Judging simply on the amount of theorems that had to be proved in leading to the account of Peano Arithmetic, PM does not differ wildly from Frege’s earlier attempt.