科研之友
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摘要
We extend and improve the result of Makkai and Pare (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 L-mu,L-omega-compact cardinals for sufficiently large it, and also show that under this assumption the lambda-pure powerful image of mu, 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.
- 出版日期2017-3
