Rathjen, M (2005) Constructive set theory and Brouwerian principles. Journal of Universal Computer Science, 11 (12). 2008 - 2033. ISSN 0948-695X
Abstract
The paper furnishes realizability models of constructive Zermelo-Fraenkel set theory, CZF, which also validate Brouwerian principles such as the axiom of continuous choice (CC), the fan theorem (FT), and monotone bar induction (BIM), and thereby determines the proof-theoretic strength of CZF augmented by these principles. The upshot is that CZF+CC+FT possesses the same strength as CZF, or more precisely, that CZF+CC+FTis conservative over CZF for 02 statements of arithmetic, whereas the addition of a restricted version of bar induction to CZF (called decidable bar induction, BID) leads to greater proof-theoretic strength in that CZF+BID proves the consistency of CZF.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2005, Graz University of Technology, Institut für Informationssysteme und Computer Medien. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Constructive set theory; Brouwerian principles; Partial combinatory algebra; Realizability |
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: | 25 Oct 2013 10:32 |
Last Modified: | 15 Sep 2014 02:50 |
Published Version: | http://dx.doi.org/10.3217/jucs-011-12-2008 |
Status: | Published |
Publisher: | Graz University of Technology, Institut für Informationssysteme und Computer Medien |
Identification Number: | 10.3217/jucs-011-12-2008 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76754 |