Cofinal types of topological directed orders

SŁawomir Solecki[1]; Stevo Todorcevic

  • [1] University of Illinois, Department of mathematics, 1409 W. green st., Urbana IL 61801 (USA), Université Paris VII-CNRS, UMR 7056, 2 place Jussieu, 75251 Paris cedex 05 (France)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 6, page 1877-1911
  • ISSN: 0373-0956

Abstract

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We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.

How to cite

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Solecki, SŁawomir, and Todorcevic, Stevo. "Cofinal types of topological directed orders." Annales de l’institut Fourier 54.6 (2004): 1877-1911. <http://eudml.org/doc/116163>.

@article{Solecki2004,
abstract = {We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.},
affiliation = {University of Illinois, Department of mathematics, 1409 W. green st., Urbana IL 61801 (USA), Université Paris VII-CNRS, UMR 7056, 2 place Jussieu, 75251 Paris cedex 05 (France)},
author = {Solecki, SŁawomir, Todorcevic, Stevo},
journal = {Annales de l’institut Fourier},
keywords = {Tukey order; analytic ideals; $\sigma $-ideals of compact sets; -ideals of compact sets; Tukey reducibility; measure and category},
language = {eng},
number = {6},
pages = {1877-1911},
publisher = {Association des Annales de l'Institut Fourier},
title = {Cofinal types of topological directed orders},
url = {http://eudml.org/doc/116163},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Solecki, SŁawomir
AU - Todorcevic, Stevo
TI - Cofinal types of topological directed orders
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 6
SP - 1877
EP - 1911
AB - We investigate the structure of the Tukey ordering among directed orders arising naturally in topology and measure theory.
LA - eng
KW - Tukey order; analytic ideals; $\sigma $-ideals of compact sets; -ideals of compact sets; Tukey reducibility; measure and category
UR - http://eudml.org/doc/116163
ER -

References

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  9. S. Solecki, Analytic ideals and their applications, Ann. Pure Appl. Logic 99 (1999), 51-72 Zbl0932.03060MR1708146
  10. S. Todorcevic, Directed sets and cofinal types, Trans. Amer. Math. Soc 290 (1985), 711-723 Zbl0592.03037MR792822
  11. S. Todorcevic, A classification of transitive relations on 1 , Proc. London Math. Soc. 73 (1996), 501-533 Zbl0870.04001MR1407459
  12. S. Todorcevic, Analytic gaps, Fund. Math 150 (1996), 55-66 Zbl0851.04002MR1387957
  13. S. Todorcevic, Definable ideals and gaps in their quotients, Set Theory (Curacao 1995, Barcelona, 1990) (1998), 213-226, Kluwer, Dordrecht Zbl0894.03026
  14. J.W. Tukey, Convergence and uniformity in topology, 1 (1940), Princeton U.P Zbl0025.09102MR2515
  15. S. Zafrany, On analytic filters and prefilters, J. Symb. Logic 55 (1990), 315-322 Zbl0705.03027MR1043560

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