According to this statement, if there were ω-sequences satisfying PA's axioms, S would hold in them. This is the hypothetical component of the modal-structural interpretation (for a detailed analysis and a precise formulation, see (Hellman 1989, pp. 16–24)). The categorical component constitutes the second step (Helman 1989, pp. 24–33). The idea is to assume that the structures of the appropriate kind are logically possible. In that case, we have that