Finite presentability of strongly finite dilators

Osamu Takaki

RAIRO - Theoretical Informatics and Applications (2010)

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

Abstract

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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.

How to cite

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Takaki, 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

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  1. J. Ad a ´ mek and J. Rosick y ´ , Locally presentable and accessible categories. Cambridge University Press, London Math. Soc. Lecture Notes Ser.189 (1994).  
  2. E.A. Cichon and S.S. Wainer, The slow-growing and the Grzegorczyk hierarchies. J. Symbolic Logic48 (1983) 399-408.  
  3. J.Y. Girard, Π 2 1 -logic, Part I; dilators. Ann. Math. Logic21 (1981) 75-219.  
  4. J.Y. Girard, Proof theory and logical complexity, Vol. 1. Bibliopolis (1987).  
  5. P.T. Johnstone, A topos-theorist looks at dilators. J. Pure Appl. Algebra58 (1989) 235-249.  
  6. A. Weiermann, A functorial property of the Aczel-Buchholz-Feferman function. J. Symbolic Logic59 (1994) 945-955.  

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