Publication detail

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

LIEBERMAN, M.

English title

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

Type

journal article in Web of Science

Language

en

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.

English 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 in English

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

Released

01.06.2020

Publisher

American Mathematical Society

Location

Providence, Rhode Island, USA

ISSN

1088-6826

Volume

148

Number

9

Pages from–to

4065–4077

Pages count

13

BIBTEX


@article{BUT164488,
  author="Michael Joseph {Lieberman},
  title="A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS",
  year="2020",
  volume="148",
  number="9",
  month="June",
  pages="4065--4077",
  publisher="American Mathematical Society",
  address="Providence, Rhode Island, USA",
  issn="1088-6826"
}