 The Axiom of Infinity asserts that all inductive cardinals are non-empty. (Recall that 0 = \(\{ \varnothing \}\), and so 0 is not empty.) The Axiom of Infinity is not a “primitive proposition” but instead to be listed as an “hypothesis” where used, that is as the antecedent of a conditional, where the consequent will be said to depend on the axiom. Technically it is not an axiom of PM as [∗120·03] is a definition, so this is just further notation in PM!