Gambino, N orcid.org/0000-0002-4257-3590 (2005) Presheaf models for constructive set theories. In: Crosilla, L and Schuster, P, (eds.) From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics. Oxford University Press , Oxford, UK , pp. 62-77. ISBN 9780198566519
Abstract
This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of algebraic set theory. It defines a general notion of what is a categorical model for CST, and shows that categories of presheaves provide examples of such models. To do so, it considers presheaves as functors with values in a category of classes. The models introduced are a counterpart of the presheaf models for intuitionistic set theories defined by Dana Scott in the 1980s. In this work, the author has to overcome the challenges intrinsic to dealing with generalized predicative formal systems rather than impredicative ones. An application to an independence result is discussed.
Metadata
Item Type: | Book Section |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2005 Oxford University Press. This is an author produced version of a paper published in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics, edited by Laura Crosilla and Peter Schuster. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | presheaves, algebraic set theory, intuitionistic set theory, independence proofs, Dana Scott |
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: | 07 Sep 2017 16:04 |
Last Modified: | 16 Jan 2018 14:15 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/acprof:oso/9780198566519.003.0004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113160 |