Accessible Images Revisited

Andrew D Brooke-Taylor, Jiri Rosicky

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
312 Downloads (Pure)


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,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.
Original languageEnglish
Pages (from-to)1317-1327
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number3
Early online date18 Nov 2016
Publication statusPublished - Mar 2017


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