A note on ordinal exponentiation and derivatives of normal functions

Mathematical Logic Quarterly 66 (3):326-335 (2020)
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Abstract

Michael Rathjen and the present author have shown that ‐bar induction is equivalent to (a suitable formalization of) the statement that every normal function has a derivative, provably in. In this note we show that the base theory can be weakened to. Our argument makes crucial use of a normal function f with and. We shall also exhibit a normal function g with and.

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10.1002/malq.201900059

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Citations of this work

Derivatives of normal functions in reverse mathematics.Anton Freund & Michael Rathjen - 2021 - Annals of Pure and Applied Logic 172 (2):102890.
Well ordering principles and -statements: A pilot study.Anton Freund - 2021 - Journal of Symbolic Logic 86 (2):709-745.

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References found in this work

Reverse mathematics and ordinal exponentiation.Jeffry L. Hirst - 1994 - Annals of Pure and Applied Logic 66 (1):1-18.
Computable aspects of the Bachmann–Howard principle.Anton Freund - 2019 - Journal of Mathematical Logic 20 (2):2050006.
The veblen functions for computability theorists.Alberto Marcone & Antonio Montalbán - 2011 - Journal of Symbolic Logic 76 (2):575 - 602.
Derivatives of normal functions in reverse mathematics.Anton Freund & Michael Rathjen - 2021 - Annals of Pure and Applied Logic 172 (2):102890.

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