Aguilera, JP, Freund, A, Rathjen, M orcid.org/0000-0003-1699-4778 et al. (1 more author) (2021) Ackermann and Goodstein go functorial. Pacific Journal of Mathematics, 313 (2). pp. 251-291. ISSN 0030-8730
Abstract
We present variants of Goodstein’s theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These variants differ from the usual Goodstein theorem in that they (necessarily) entail the existence of complex infinite objects. As part of our proof, we show that the Veblen hierarchy of normal functions on the ordinals is closely related to an extension of the Ackermann function by direct limits.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This item is protected by copyright, all rights reserved. This is an author produced version of an article published in Pacific Journal of Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Ackermann function, Goodstein's theorem, number representation, reverse mathematics, Veblen hierarchy, well-ordering principles |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Oct 2021 09:32 |
Last Modified: | 07 Dec 2021 05:32 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers (MSP) |
Identification Number: | 10.2140/pjm.2021.313.251 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178744 |