Publication result detail

Tameness, powerful images, and large cardinals

LIEBERMAN, M.; BONEY, W.

Original Title

Tameness, powerful images, and large cardinals

English Title

Tameness, powerful images, and large cardinals

Type

Scopus Article

Original Abstract

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].

English abstract

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].

Keywords

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

Key words in English

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

Authors

LIEBERMAN, M.; BONEY, W.

RIV year

2021

Released

01.04.2021

Publisher

World Scientific

Location

Singapore

ISBN

0219-0613

Periodical

Journal of Mathematical Logic

Volume

21

Number

1

State

Republic of Singapore

Pages from

1

Pages to

18

Pages count

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"
}