Hanf numbers via accessible images

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Authors

LIEBERMAN Michael ROSICKÝ Jiří

Year of publication 2017
Type Article in Periodical
Magazine / Source Logical Methods in Computer Science
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.23638/LMCS-13(2:11)2017
Doi http://dx.doi.org/10.23638/LMCS-13(2:11)2017
Keywords accessible category; powerful image; Hanf number; strongly compact cardinal
Description 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.
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