A category-theoretic characterization of almost measurable cardinals

Lieberman, Michael

doi:10.1090/proc/15076

A category-theoretic characterization of almost measurable cardinals
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Proc. Amer. Math. Soc. 148 (2020), 4065-4077 Request permission

Abstract:

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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