Yes sorry, dominant means strictly better in some sense, but may be equal in many objectives.

> Every solution in the Pareto front set dominates every solution not in that set

Not quite – for each solution not in the set, there exists a solution in the set that dominates it. For instance a front with (0,2) (1,1) (2,0) would not have (1,0). While (0,2) doesn't dominate (1,0), something else does.