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Accessible Images Revisited

Research output: Contribution to journalArticle

  • Andrew D Brooke-Taylor
  • Jiri Rosicky
Original languageEnglish
Pages (from-to)1317-1327
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number3
Early online date18 Nov 2016
DateAccepted/In press - 6 Mar 2016
DateE-pub ahead of print - 18 Nov 2016
DatePublished (current) - Mar 2017


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.

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