# Finite presentability of strongly finite dilators

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 34, Issue: 6, page 425-431
- ISSN: 0988-3754

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topTakaki, Osamu. "Finite presentability of strongly finite dilators." RAIRO - Theoretical Informatics and Applications 34.6 (2010): 425-431. <http://eudml.org/doc/221946>.

@article{Takaki2010,

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.
},

author = {Takaki, Osamu},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Dilator; ordinal notation; finite presentability.; finite presentability; strongly finite dilator; endofunctors; category of ordinals; category of dilators},

language = {eng},

month = {3},

number = {6},

pages = {425-431},

publisher = {EDP Sciences},

title = {Finite presentability of strongly finite dilators},

url = {http://eudml.org/doc/221946},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Takaki, Osamu

TI - Finite presentability of strongly finite dilators

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 6

SP - 425

EP - 431

AB -
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.

LA - eng

KW - Dilator; ordinal notation; finite presentability.; finite presentability; strongly finite dilator; endofunctors; category of ordinals; category of dilators

UR - http://eudml.org/doc/221946

ER -

## References

top- J. Ad $\stackrel{\xb4}{\mathrm{a}}$mek and J. Rosick $\stackrel{\xb4}{\mathrm{y}}$, Locally presentable and accessible categories. Cambridge University Press, London Math. Soc. Lecture Notes Ser.189 (1994).
- E.A. Cichon and S.S. Wainer, The slow-growing and the Grzegorczyk hierarchies. J. Symbolic Logic48 (1983) 399-408. Zbl0567.03020
- J.Y. Girard, ${\Pi}_{2}^{1}$-logic, Part I; dilators. Ann. Math. Logic21 (1981) 75-219. Zbl0496.03037
- J.Y. Girard, Proof theory and logical complexity, Vol. 1. Bibliopolis (1987). Zbl0635.03052
- P.T. Johnstone, A topos-theorist looks at dilators. J. Pure Appl. Algebra58 (1989) 235-249. Zbl0675.18005
- A. Weiermann, A functorial property of the Aczel-Buchholz-Feferman function. J. Symbolic Logic59 (1994) 945-955. Zbl0808.03039

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