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arXiv · 2202.05611

Weak and Strong Versions of Effective Transfinite Recursion

Patrick Uftring
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Abstract

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

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Patrick Uftring. 2022-02-11. Weak and Strong Versions of Effective Transfinite Recursion. https://doi.org/10.1016/j.apal.2022.103232

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