  We study the effect of interactions on 2D fermionic symmetry-protected
topological (SPT) phases using the recently proposed braiding statistics
approach. We focus on a simple class of examples: superconductors with a Z2
Ising symmetry. Although these systems are classified by Z in the
noninteracting limit, our results suggest that the classification collapses to
Z8 in the presence of interactions -- consistent with previous work that
analyzed the stability of the edge. Specifically, we show that there are at
least 8 different types of Ising superconductors that cannot be adiabatically
connected to one another, even in the presence of strong interactions. In
addition, we prove that each of the 7 nontrivial superconductors have protected
edge modes.
