一句话：在大基数假设下用可及函子的可及像，将 AEC 的 Hanf 数结果推广到可及范畴，并证明度量 AEC 强 d-tame。
本文研究抽象初等类（AEC）与可及范畴中结构性质（如 joint embedding 与 amalgamation）的 Hanf 数提升问题。作者基于如下事实：若存在 proper class of almost strongly compact cardinals，则任意 accessible functor 的 powerful image 仍是 accessible。利用这一可及性结果，作者把 Baldwin 与 Boney 最近的 Hanf 数计算从 AEC 推广到可及范畴：若这些性质对直到足够大基数的模型成立，则对所有大小的模型成立。此外，在上述大基数假设下，论文证明每个度量 AEC 都是 strongly d-tame，从而加强了 Boney 与 Zambrano 的结果，并指出进一步推广的路径。
We present several new model-theoretic applications of the fact that, under the assumption that there exists a proper class of almost strongly compact cardinals, the powerful image of any accessible functor is accessible. In particular, we generalize to the context of accessible categories the recent Hanf number computations of Baldwin and Boney, namely that in an abstract elementary class (AEC) if the joint embedding and amalgamation properties hold for models of size up to a sufficiently large cardinal, then they hold for models of arbitrary size. Moreover, we prove that, under the above-mentioned large cardinal assumption, every metric AEC is strongly d-tame, strengthening a result of Boney and Zambrano and pointing the way to further generalizations.Comment: v1: 15 pages. v2: 13 pages, reformatted with minor edits. v3: 15 pages, title changed from "Bootstrapping structural properties, via accessible images," proofs expanded, definitions clarified in response to referees' feedback. v4: 15 pages, dedication added. v5: 15 pages, minor corrections, in press