Detail publikace

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

LIEBERMAN, M.

Anglický název

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

01.06.2020

Nakladatel

American Mathematical Society

Místo

Providence, Rhode Island, USA

ISSN

1088-6826

Ročník

148

Číslo

9

Strany od–do

4065–4077

Počet stran

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"
}