Publication detail

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

LIEBERMAN, M.

Original Title

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

Almost measurable cardinals, accessible categories, abstract elementary classes, Galois types, locality

Authors

LIEBERMAN, M.

Released

1. 6. 2020

Publisher

American Mathematical Society

Location

Providence, Rhode Island, USA

ISBN

1088-6826

Periodical

Proceedings of the American Mathematical Society

Year of study

148

Number

9

State

United States of America

Pages from

4065

Pages to

4077

Pages count

13

URL

https://www.ams.org/journals/proc/2020-148-09/S0002-9939-2020-15076-9/

BibTex

@article{BUT164488,
  author="Michael Joseph {Lieberman}",
  title="A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS",
  journal="Proceedings of the American Mathematical Society",
  year="2020",
  volume="148",
  number="9",
  pages="4065--4077",
  doi="10.1090/proc/15076",
  issn="1088-6826",
  url="https://www.ams.org/journals/proc/2020-148-09/S0002-9939-2020-15076-9/"
}