no. 6
Cofinal types of topological directed orders
[Types cofinaux d'espaces topologiques ordonnés filtrants]
Solecki, SŁawomir1 ; 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)
Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1877-1911.

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.

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

DOI : 10.5802/aif.2070
Classification : 03E05, 06A07, 03E15, 03E17, 22A26
Keywords: Tukey order, analytic ideals, $\sigma $-ideals of compact sets
Mot clés : Ordre de Tukey, idéaux analytiques, $\sigma $-ideaux d’ensembles compacts
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) 
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Solecki, SŁawomir; Todorcevic, Stevo. Cofinal types of topological directed orders. Annales de l'Institut Fourier, Tome 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 ℵ 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

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