Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T02:12:44.768Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite presentability of strongly finite dilators

Published online by Cambridge University Press:  15 April 2002

Osamu Takaki
Osamu Takaki*
Affiliation:
The Japan Society for the Promotion of Science, Japan; (takaki@i.h.kyoto-u.ac.jp.)
Get access

Abstract

In this paper, we establish the following results: (i) every strongly finite dilator is finitely presentable in the category of endofunctors on the category of ordinals; (ii) a dilator F is strongly finite if and only if F is finitely presentable in the category of dilators.

Keywords

Dilatorordinal notationfinite presentability.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 6 , November 2000 , pp. 425 - 431
Copyright
© EDP Sciences, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J. Ad $\acute{{\rm a}}$ mek and J. Rosick $\acute{{\rm y}}$ , Locally presentable and accessible categories. Cambridge University Press, London Math. Soc. Lecture Notes Ser. 189 (1994).
Cichon, E.A. and Wainer, S.S., The slow-growing and the Grzegorczyk hierarchies. J. Symbolic Logic 48 (1983) 399-408. CrossRef
J.Y. Girard, $\Pi^1_2$ -logic, Part I; dilators. Ann. Math. Logic 21 (1981) 75-219.
J.Y. Girard, Proof theory and logical complexity, Vol. 1. Bibliopolis (1987).
Johnstone, P.T., A topos-theorist looks at dilators. J. Pure Appl. Algebra 58 (1989) 235-249. CrossRef
Weiermann, A., A functorial property of the Aczel-Buchholz-Feferman function. J. Symbolic Logic 59 (1994) 945-955. CrossRef