Full Reflection of Stationary Sets at Regular Cardinals

0. Introduction. A stationary subset S of a regular uncountable cardinal κ reflects fully at regular cardinals if for every stationary set T ⊆ κ of higher order consisting of regular cardinals there exists an α ∈ T such that S ∩ α is a stationary subset of α. We prove that the Axiom of Full Reflection which states that every stationary set reflects fully at regular cardinals, together with the existence of n-Mahlo cardinals is equiconsistent with the existence of Πn-indescribable cardinals. We also state the appropriate generalization for greatly Mahlo cardinals.