Publication details

Tameness, powerful images, and large cardinals



Year of publication 2021
Type Article in Periodical
Magazine / Source Journal of Mathematical Logic
MU Faculty or unit

Faculty of Science

Keywords Weakly compact cardinals; accessible categories; abstract elementary classes; Galois types; locality; tameness
Description We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of accessible functors. In the process, we show that these properties are also equivalent to various forms of tameness for abstract elementary classes. This systematizes and extends results of [W. Boney and S. Unger, Large cardinal axioms from tameness in AECs, Proc. Amer. Math. Soc. 145(10) (2017) 4517-4532; A. Brooke-Taylor and J. Rosicky, Accessible images revisited, Proc. AMS 145(3) (2016) 1317-1327; M. Lieberman, A category-theoretic characterization of almost measurable cardinals (Submitted, 2018),; M. Lieberman and J. Rosicky, Classification theory for accessible categories. J. Symbolic Logic 81(1) (2016) 1647-1648].

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