Accessible Images Revisited

Andrew D Brooke-Taylor, Jiri Rosicky

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

7 Citations (Scopus)
255 Downloads (Pure)

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,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
Volume145
Issue number3
Early online date18 Nov 2016
DOIs
Publication statusPublished - Mar 2017

Fingerprint

Dive into the research topics of 'Accessible Images Revisited'. Together they form a unique fingerprint.

Cite this