A category-theoretic characterization of almost measurable cardinals
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Proceedings of the American Mathematical Society |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1090/proc/15076 |
| Doi | http://dx.doi.org/10.1090/proc/15076 |
| Keywords | Almost measurable cardinals; accessible categories; abstract elementary classes; Galois-types; locality |
| Description | Through careful analysis of an argument of [Proc. Amer. Math. Soc. 145 (2017), pp. 1317-1327], we show that the powerful image of any accessible functor is closed under colimits of kappa-chains, kappa a sufficiently large almost measurable cardinal. This condition on powerful images, by methods resembling those of [J. Symb. Log. 81 (2016), pp. 151-165], implies kappa-locality of Galois-types. As this, in turn, implies sufficient measurability of kappa, via [Proc. Amer. Math. Soc. 145 (2017), pp. 4517-4532], we obtain an equivalence: a purely category-theoretic characterization of almost measurable cardinals. |
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