 “By a ‘progression’ we mean a series which is like the series of the inductive cardinals in order of magnitude (assuming that all the inductive cardinals exist) i.e. a series whose terms can be called \(1_R, 2_R, 3_R, \ldots \nu_R, \ldots \). It is not convenient to define a progression as a series which is ordinally similar to that of the inductive cardinals, both because this definition only applies if we assume the axiom of infinity, and because we have in any case to show that (assuming the axiom of infinity) the series of inductive cardinals has certain properties, which can be used to afford a direct definition of progressions.” (PM II, 245)