 This Axiom of Infinity asserts that all inductive cardinals are non-empty. (Recall that \(0 = \{\emptyset \}\), and so 0 is not empty.) The axiom 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 is not an axiom of PM as ∗120·03 is a definition, so this is just further defined notation in PM!