Detail publikačního výsledku

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

LIEBERMAN, M.

Originální název

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

Anglický název

A CATEGORY-THEORETIC CHARACTERIZATION OF ALMOST MEASURABLE CARDINALS

Druh

Článek WoS

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

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

Klíčová slova v angličtině

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

Autoři

LIEBERMAN, M.

Rok RIV

2021

Vydáno

01.06.2020

Nakladatel

American Mathematical Society

Místo

Providence, Rhode Island, USA

ISSN

1088-6826

Periodikum

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Svazek

148

Číslo

9

Stát

Spojené státy americké

Strany od

4065

Strany do

4077

Strany počet

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="0002-9939",
  url="https://www.ams.org/journals/proc/2020-148-09/S0002-9939-2020-15076-9/"
}