In FS one can define all finite levels of the classical Tarskian hierarchy, but FS isn’t strong enough to allow one to recover any of its transfinite levels. Indeed, Halbach (1994) determined its proof-theoretic strength to be precisely that of the theory of ramified truth for all finite levels (i.e., finitely iterated T(PA); see Section 3.4) or, equivalently, the theory of ramified analysis for all finite levels. If either direction of the rule is dropped but the other kept, FS retains its proof-theoretic strength (Sheard 2001).