Detail publikačního výsledku

Tameness, powerful images, and large cardinals

LIEBERMAN, M.; BONEY, W.

Originální název

Tameness, powerful images, and large cardinals

Anglický název

Tameness, powerful images, and large cardinals

Druh

Článek Scopus

Originální abstrakt

We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of accessible functors. In the process, we show that these properties are also equivalent to various forms of tameness for abstract elementary classes. This systematizes and extends results of [W. Boney and S. Unger, Large cardinal axioms from tameness in AECs, Proc. Amer. Math. Soc. 145(10) (2017) 4517-4532; A. Brooke-Taylor and J. Rosicky, Accessible images revisited, Proc. AMS 145(3) (2016) 1317-1327; M. Lieberman, A category-theoretic characterization of almost measurable cardinals (Submitted, 2018), http://arxiv.org/abs/1809.06963; M. Lieberman and J. Rosicky, Classification theory for accessible categories. J. Symbolic Logic 81(1) (2016) 1647-1648].

Anglický abstrakt

We provide comprehensive, level-by-level characterizations of large cardinals, in the range from weakly compact to strongly compact, by closure properties of powerful images of accessible functors. In the process, we show that these properties are also equivalent to various forms of tameness for abstract elementary classes. This systematizes and extends results of [W. Boney and S. Unger, Large cardinal axioms from tameness in AECs, Proc. Amer. Math. Soc. 145(10) (2017) 4517-4532; A. Brooke-Taylor and J. Rosicky, Accessible images revisited, Proc. AMS 145(3) (2016) 1317-1327; M. Lieberman, A category-theoretic characterization of almost measurable cardinals (Submitted, 2018), http://arxiv.org/abs/1809.06963; M. Lieberman and J. Rosicky, Classification theory for accessible categories. J. Symbolic Logic 81(1) (2016) 1647-1648].

Klíčová slova

weakly compact cardinals; accessible categories; abstract elementary classes; Galois types; locality; tameness

Klíčová slova v angličtině

weakly compact cardinals; accessible categories; abstract elementary classes; Galois types; locality; tameness

Autoři

LIEBERMAN, M.; BONEY, W.

Rok RIV

2021

Vydáno

01.04.2021

Nakladatel

World Scientific

Místo

Singapore

ISSN

0219-0613

Periodikum

Journal of Mathematical Logic

Svazek

21

Číslo

1

Stát

Singapurská republika

Strany od

1

Strany do

18

Strany počet

18

URL

https://www.worldscientific.com/doi/10.1142/S0219061320500245

BibTex

@article{BUT164522,
  author="Michael Joseph {Lieberman} and Will {Boney}",
  title="Tameness, powerful images, and large cardinals",
  journal="Journal of Mathematical Logic",
  year="2021",
  volume="21",
  number="1",
  pages="1--18",
  doi="10.1142/S0219061320500245",
  issn="0219-0613",
  url="https://www.worldscientific.com/doi/10.1142/S0219061320500245"
}