Freund, A. and Rathjen, M. orcid.org/0000-0003-1699-4778 (2023) Well ordering principles for iterated 511-comprehension. Selecta Mathematica, 29. 76. ISSN 1022-1824
Abstract
We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated 1 1- comprehension and the existence of admissible sets, over weak base theories. Our work extends a previous result on the non-iterated case, which had been conjectured in Montalbán’s “Open questions in reverse mathematics" (Bull Symb Log 17(3):431– 454, 2011). This previous result has already been applied to the reverse mathematics of combinatorial and set theoretic principles. The present paper is a significant contribution to a general approach that connects these fields.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Well ordering principles; Ordinal collapsing functions; Iterated comprehension; Transfinite recursion; Admissible sets; Dilators; Ordinal analysis; Reverse mathematics |
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: | 13 Dec 2023 10:32 |
Last Modified: | 13 Dec 2023 10:32 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00029-023-00879-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206557 |