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A note on ordinal exponentiation and derivatives of normal functions

Freund, Anton (2024)
A note on ordinal exponentiation and derivatives of normal functions.
In: Mathematical Logic Quarterly, 2020, 66 (3)
doi: 10.26083/tuprints-00016165
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: A note on ordinal exponentiation and derivatives of normal functions
Language: English
Date: 26 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2020
Place of primary publication: Weinheim
Publisher: Wiley-VCH
Journal or Publication Title: Mathematical Logic Quarterly
Volume of the journal: 66
Issue Number: 3
DOI: 10.26083/tuprints-00016165
Corresponding Links:
Origin: Secondary publication DeepGreen

Michael Rathjen and the present author have shown that Π11‐bar induction is equivalent to (a suitable formalization of) the statement that every normal function has a derivative, provably in ACA0. In this note we show that the base theory can be weakened to RCA0. Our argument makes crucial use of a normal function f with f(α)≤1+α² and f′(α)=ωωα. We shall also exhibit a normal function g with g(α)≤1+α·2 and g′(α)=ω1+α.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-161654
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Logic
Date Deposited: 26 Jan 2024 13:45
Last Modified: 27 Feb 2024 14:00
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/16165
PPN: 51584649X
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