Brooke-Taylor, A and Rosicky, J (2017) Accessible images revisited. Proceedings of the American Mathematical Society, 145 (3). pp. 1317-1327. ISSN 0002-9939
Abstract
We extend and improve the result of Makkai and Paré (1989) that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption to the existence of Lμ,ω-compact cardinals for sufficiently large μ, and also show that under this assumption the λ-pure powerful image of F is accessible. From the first of these statements, we obtain that the tameness of every Abstract Elementary Class follows from a weaker large cardinal assumption than was previously known. We provide two ways of employing the large cardinal assumption to prove each result — one by a direct ultraproduct construction and one using the machinery of elementary embeddings of the set-theoretic universe.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 American Mathematical Society. This is an author produced version of a paper published in Proceedings of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
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 Oct 2016 15:06 |
Last Modified: | 25 Apr 2017 04:30 |
Published Version: | https://doi.org/10.1090/proc/13190 |
Status: | Published |
Publisher: | American Mathematical Society |
Identification Number: | 10.1090/proc/13190 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103969 |