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Abstract
We extend and improve the result of Makkai and Paré 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,ωcompact cardinals for sufficiently large μ, and also show that under this assumption the λpure 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.
Original language  English 

Pages (fromto)  13171327 
Number of pages  11 
Journal  Proceedings of the American Mathematical Society 
Volume  145 
Issue number  3 
Early online date  18 Nov 2016 
DOIs  
Publication status  Published  Mar 2017 
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Dive into the research topics of 'Accessible Images Revisited'. Together they form a unique fingerprint.Projects
 1 Finished

Bringing set theory and algebraic topology together.
Rasappan, R.
21/10/13 → 20/06/16
Project: Research