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 |
| Abstract: | 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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