## A category-theoretic characterization of almost measurable cardinals

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- by Michael Lieberman
- Proc. Amer. Math. Soc.
**148**(2020), 4065-4077 - DOI: https://doi.org/10.1090/proc/15076
- Published electronically: June 1, 2020
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## 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.## References

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## Bibliographic Information

**Michael Lieberman**- Affiliation: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic; and Department of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic
- MR Author ID: 938223
- Email: qmlieberman@vutbr.cz
- Received by editor(s): October 3, 2018
- Received by editor(s) in revised form: December 13, 2019
- Published electronically: June 1, 2020
- Additional Notes: The author was supported by the Grant Agency of the Czech Republic under the grant P201/12/G028.
- Communicated by: Heike Mildenberger
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 4065-4077 - MSC (2010): Primary 03E55, 18C35; Secondary 03E75, 03C20, 03C48, 03C75
- DOI: https://doi.org/10.1090/proc/15076
- MathSciNet review: 4127849