Feferman (1991) showed that KF is proof-theoretically equivalent to the theory of ramified analysis through all levels below \(\varepsilon_0\), the limit of the sequence \(\omega , \omega^{\omega}, \omega^{\omega^{ \omega} },\ldots\), or a theory of ramified truth through the same ordinals. This result shows that in KF exactly \(\varepsilon_0\) many levels of the classical Tarskian hierarchy in its axiomatized form can be recovered. Thus KF is far stronger than FS, let alone T(PA). Feferman (1991) devised also a strengthening of KF that is as strong as full predicative analysis, that is ramified analysis or truth up to the ordinal \(\Gamma_0\).