Michael Lieberman ; Jiri Rosicky - Hanf numbers via accessible images

lmcs:2190 - Logical Methods in Computer Science, June 23, 2017, Volume 13, Issue 2 - https://doi.org/10.23638/LMCS-13(2:11)2017
Hanf numbers via accessible imagesArticle

Authors: Michael Lieberman ; Jiri Rosicky

    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.

    Volume: Volume 13, Issue 2
    Published on: June 23, 2017
    Accepted on: May 23, 2017
    Submitted on: June 23, 2017
    Keywords: Mathematics - Logic,Mathematics - Category Theory,03C95, 03C52, 18C35, 03E55

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