Publication details
Tameness, powerful images, and large cardinals
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Logic |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1142/S0219061320500245 |
| Doi | http://dx.doi.org/10.1142/S0219061320500245 |
| 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), http://arxiv.org/abs/1809.06963; M. Lieberman and J. Rosicky, Classification theory for accessible categories. J. Symbolic Logic 81(1) (2016) 1647-1648]. |