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Working in the context of reverse mathematics, we give a fine-grainedcharacterization result on the strength of two possible definitions forEffective Transfinite Recursion used in literature. Moreover, we show that$\Pi^0_2$-induction along a well-order $X$ is equivalent to the statement thatthe exponentiation of any well-order to the power of $X$ is well-founded.

Weak and Strong Versions of Effective Transfinite Recursion