Cofinal types of topological directed orders
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 1877-1911.

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

On étudie la structure de l'ordre de Tukey sur les ensembles ordonnés filtrants qui apparaissent naturellement en topologie et en théorie de la mesure.

DOI: 10.5802/aif.2070
Classification: 03E05,  06A07,  03E15,  03E17,  22A26
Keywords: Tukey order, analytic ideals, σ-ideals of compact sets
Solecki, SŁawomir 1; Todorcevic, Stevo 

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)
@article{AIF_2004__54_6_1877_0,
     author = {Solecki, S{\L}awomir and Todorcevic, Stevo},
     title = {Cofinal types of topological directed orders},
     journal = {Annales de l'Institut Fourier},
     pages = {1877--1911},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {6},
     year = {2004},
     doi = {10.5802/aif.2070},
     zbl = {1071.03034},
     mrnumber = {2134228},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2070/}
}
TY  - JOUR
AU  - Solecki, SŁawomir
AU  - Todorcevic, Stevo
TI  - Cofinal types of topological directed orders
JO  - Annales de l'Institut Fourier
PY  - 2004
DA  - 2004///
SP  - 1877
EP  - 1911
VL  - 54
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2070/
UR  - https://zbmath.org/?q=an%3A1071.03034
UR  - https://www.ams.org/mathscinet-getitem?mr=2134228
UR  - https://doi.org/10.5802/aif.2070
DO  - 10.5802/aif.2070
LA  - en
ID  - AIF_2004__54_6_1877_0
ER  - 
%0 Journal Article
%A Solecki, SŁawomir
%A Todorcevic, Stevo
%T Cofinal types of topological directed orders
%J Annales de l'Institut Fourier
%D 2004
%P 1877-1911
%V 54
%N 6
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.2070
%R 10.5802/aif.2070
%G en
%F AIF_2004__54_6_1877_0
Solecki, SŁawomir; Todorcevic, Stevo. Cofinal types of topological directed orders. Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 1877-1911. doi : 10.5802/aif.2070. http://www.numdam.org/articles/10.5802/aif.2070/

[1] J.P.R. Christensen Topology and Borel Structure, North-Holland/Elsevier, 1974 | MR | Zbl

[2] I. Farah Analytic Quotients, Mem. Amer. Math. Soc, Volume 148 (2000) no. 702 | MR | Zbl

[3] D.H. Fremlin The partially ordered sets of measure theory and Tukey's ordering, Note di Matematica, Volume 11 (1991), pp. 177-214 | MR | Zbl

[4] D.H. Fremlin Families of compact sets and Tukey ordering, Atti. Sem. Mat. Fiz, Volume 39 (1991), pp. 29-50 | MR | Zbl

[5] J.R. Isbell Seven cofinal types, J. London Math. Soc, Volume 4 (1972), pp. 651-654 | MR | Zbl

[6] A.S. Kechris Classical Descriptive Set Theory, Springer, 1995 | MR | Zbl

[7] A.S. Kechris; A. Louveau; W.H. Woodin The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc, Volume 301 (1987), pp. 263-288 | MR | Zbl

[8] A. Louveau; B. Veli{#x010D;}kovi{#x0107;} Analytic ideals and cofinal types, Ann. Pure Appl. Logic, Volume 99 (1999), pp. 171-195 | MR | Zbl

[9] S. Solecki Analytic ideals and their applications, Ann. Pure Appl. Logic, Volume 99 (1999), pp. 51-72 | MR | Zbl

[10] S. Todorcevic Directed sets and cofinal types, Trans. Amer. Math. Soc, Volume 290 (1985), pp. 711-723 | MR | Zbl

[11] S. Todorcevic A classification of transitive relations on 1 , Proc. London Math. Soc., Volume 73 (1996), pp. 501-533 | MR | Zbl

[12] S. Todorcevic Analytic gaps, Fund. Math, Volume 150 (1996), pp. 55-66 | EuDML | MR | Zbl

[13] S. Todorcevic Definable ideals and gaps in their quotients, Set Theory (Curacao 1995, Barcelona, 1990) (1998), pp. 213-226 | MR | Zbl

[14] J.W. Tukey Convergence and uniformity in topology, Ann. Math. Studies, 1, Princeton U.P, 1940 | JFM | MR | Zbl

[15] S. Zafrany On analytic filters and prefilters, J. Symb. Logic, Volume 55 (1990), pp. 315-322 | MR | Zbl

Cited by Sources: