  In the context of reverse mathematics, effective transfinite recursion refers
to a principle that allows us to construct sequences of sets by recursion along
arbitrary well orders, provided that each set is $\Delta^0_1$-definable
relative to the previous stages of the recursion. It is known that this
principle is provable in $\mathbf{ACA}_0$. In the present note, we argue that a
common formulation of effective transfinite recursion is too restrictive. We
then propose a more liberal formulation, which appears very natural and is
still provable in $\mathbf{ACA}_0$.
