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Rathjen, M (2013) Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. Annals of Pure and Applied Logic, 165 (2). 563 - 572. ISSN 0168-0072
Abstract
In recent years the question of whether adding the limited principle of omniscience, LPO, to constructive Zermelo–Fraenkel set theory, CZF, increases its strength has arisen several times. As the addition of excluded middle for atomic formulae to CZF results in a rather strong theory, i.e. much stronger than classical Zermelo set theory, it is not obvious that its augmentation by LPO would be proof-theoretically benign. The purpose of this paper is to show that CZF+RDC+LPO has indeed the same strength as CZF, where RDC stands for relativized dependent choice. In particular, these theories prove the same View the MathML source theorems of arithmetic.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013 Elsevier B.V. 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: | Constructive set theory; Limited principle of omniscience; Bar induction; 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 12:49 |
Last Modified: | 15 Jan 2018 23:35 |
Published Version: | http://dx.doi.org/10.1016/j.apal.2013.08.001 |
Status: | Published |
Publisher: | Elsevier Masson |
Identification Number: | 10.1016/j.apal.2013.08.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:81598 |
Available Versions of this Item
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Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. (deposited 01 Oct 2013 10:58)
- Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. (deposited 11 Dec 2014 12:49) [Currently Displayed]