PAKHOMOV, F., RATHJEN, M. orcid.org/0000-0003-1699-4778 and ROSSEGGER, D. (2025) FEFERMAN’S COMPLETENESS THEOREM. Bulletin of Symbolic Logic. ISSN: 1079-8986
Abstract
Feferman proved in 1962 [Fef62] that any arithmetical theorem is a consequence of a suitable transfinite iteration of full uniform reflection of PA. This result is commonly known as Feferman’s completeness theorem. The purpose of this paper is twofold. On the one hand this is an expository paper, giving two new proofs of Feferman’s completeness theorem that, we hope, shed light on this mysterious and often overlooked result. On the other hand, we combine one of our proofs with results from computable structure theory due to Ash and Knight to give sharp bounds on the order types of well-orders necessary to attain the completeness for levels of the arithmetical hierarchy.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | This is an author produced version of an article published in Bulletin of Symbolic Logic, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
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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) |
| Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
| Date Deposited: | 06 Oct 2025 11:50 |
| Last Modified: | 10 Oct 2025 15:09 |
| Status: | Published online |
| Publisher: | Cambridge University Press (CUP) |
| Identification Number: | 10.1017/bsl.2025.2 |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:232469 |

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