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Rathjen, M (2014) Relativized ordinal analysis: The case of Power Kripke-Platek set theory. Annals of Pure and Applied Logic, 165 (1). 316 - 339. ISSN 0168-0072
Abstract
The paper relativizes the method of ordinal analysis developed for Kripke-Platek set theory to theories which have the power set axiom. We show that it is possible to use this technique to extract information about Power Kripke-Platek set theory, KP (P). As an application it is shown that whenever KP (P) + AC proves a Π statement then it holds true in the segment V of the von Neumann hierarchy, where τ stands for the Bachmann-Howard ordinal.
Metadata
| Item Type: | Article |
|---|---|
| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | (c) 2013, Elsevier Masson. This is an author produced version of a paper published in Annals of Pure and Applied Logic. Uploaded in accordance with the publisher's self-archiving policy. |
| Keywords: | Ordinal analysis; Ordinal representation systems; Power Kripke-Platek set theory; Power-admissible set; Proof-theoretic strength |
| 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) |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 11 Dec 2014 14:01 |
| Last Modified: | 21 Apr 2015 19:54 |
| Published Version: | http://dx.doi.org/10.1016/j.apal.2013.07.016 |
| Status: | Published |
| Publisher: | Elsevier Masson |
| Identification Number: | 10.1016/j.apal.2013.07.016 |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82218 |
Available Versions of this Item
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Relativized ordinal analysis: The case of Power Kripke-Platek set theory. (deposited 01 Oct 2013 10:55)
- Relativized ordinal analysis: The case of Power Kripke-Platek set theory. (deposited 11 Dec 2014 14:01) [Currently Displayed]
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