A category-theoretic characterization of almost measurable cardinals

Michael Lieberman

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arXiv · 1809.05953

A category-theoretic characterization of almost measurable cardinals

Michael Lieberman

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Abstract

Through careful analysis of an argument of Brooke-Taylor and Rosicky, we show that the powerful image of any accessible functor is closed under colimits of $κ$-chains, $κ$ a sufficiently large almost measurable cardinal. This condition on powerful images, by methods resembling those of Lieberman and Rosicky, implies $κ$-locality of Galois types. As this, in turn, implies sufficient measurability of $κ$, via a paper of Boney and Unger, we obtain an equivalence: a purely category-theoretic characterization of almost measurable cardinals.

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BibTeX RIS

Michael Lieberman. 2019-12-13. A category-theoretic characterization of almost measurable cardinals. https://arxiv.org/abs/1809.05953

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