Rathjen, M and Swan, AW (2020) Lifschitz Realizability as a Topological Construction. The Journal of Symbolic Logic, 85 (4). pp. 1342-1375. ISSN 0022-4812
Abstract
We develop a number of variants of Lifschitz realizability for CZF by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with variants of the lesser limited principle of omniscience including consistency with unique Church’s thesis, consistency with some Brouwerian principles and variants of the numerical existence property.
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Copyright, Publisher and Additional Information: | This article has been published in a revised form in The Journal of Symbolic Logic [https://doi.org/10.1017/jsl.2021.1]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © The Association for Symbolic Logic 2021 | ||||
Keywords: | realizability; constructive set theory; topological models | ||||
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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) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 25 Jan 2021 15:44 | ||||
Last Modified: | 24 Jun 2021 11:06 | ||||
Status: | Published | ||||
Publisher: | Cambridge University Press | ||||
Identification Number: | https://doi.org/10.1017/jsl.2021.1 |