Proof-theoretic strengths of the well-ordering principles

In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions $$\mathsf {g}$$ on ordinals is shown to be equal to the least fixed point of $$\mathsf {g}$$ . Moreover corrections to the previous paper (Arai in Arch Math Log 57:649–664, 2017) are made.