Frittaion, E and Rathjen, M (2020) Extensional realizability for intuitionistic set theory. Journal of Logic and Computation. exaa087. ISSN 0955-792X
Abstract
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving rise to a realizability universe Vex(A) in which the axiom of choice in all finite types, ACFT, is realized, where A stands for an arbitrary partial combinatory algebra. This construction furnishes ‘inner models’ of many set theories that additionally validate ACFT, in particular it provides a self-validating semantics for CZF (constructive Zermelo–Fraenkel set theory) and IZF (intuitionistic Zermelo–Fraenkel set theory). One can also add large set axioms and many other principles.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. Published by Oxford University Press. All rights reserved. This is an author produced version of an article, published in Journal of Logic and Computation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Intuitionistic, constructive, set theory, realizability, extensionality |
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) |
Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Jan 2021 15:59 |
Last Modified: | 30 Dec 2021 01:38 |
Status: | Published online |
Publisher: | Oxford University Press (OUP) |
Identification Number: | 10.1093/logcom/exaa087 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:170280 |