Weak and Strong Versions of Effective Transfinite Recursion

DOI10.1016/J.APAL.2022.103232arXiv2202.05611MaRDI QIDQ6390836

Publication date: 11 February 2022

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

P i_{2}^{0}

-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.

Mathematics Subject Classification ID

Foundations of classical theories (including reverse mathematics) (03B30) Second- and higher-order arithmetic and fragments (03F35) Recursive ordinals and ordinal notations (03F15)

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