Heifetz, Meier and Schipper [Heifetz, A., Meier, M., Schipper, B.C., 2006a. Interactive unawareness, J. Econ. Theory 130, 78–94; Heifetz, A., Meier, M., Schipper, B.C., 2006b. Unawareness, beliefs and games. Mimeo] introduced unawareness structures. These are generalized state-space models that allow for non-trivial unawareness among several individuals and strong properties of knowledge. We show that a canonical unawareness structure arises naturally if states consist of maximally consistent sets of formulas in an appropriate axiom system. As a corollary, we obtain a strong soundness and completeness theorem for this axiom system with respect to the class of unawareness structures.