Factoring onto Z ^d subshifts with the finite extension property

We define the finite extension property for d-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by the first author, and we prove that this property is invariant under topological conjugacy. Moreover, we prove that for every d, everyd-dimensional block gluing subshift factors onto every d-dimensional shift of finite type with strictly lower entropy, a fixed point, and the finite extension property. This result extends a theorem from [Trans. Amer. Math. Soc. 362 (2010), 4617–4653], which requires that the factor contain a safe symbol.