Cofinal types of topological directed orders
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, p. 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 : https://doi.org/10.5802/aif.2070
Classification:  03E05,  06A07,  03E15,  03E17,  22A26
Keywords: Tukey order, analytic ideals, σ-ideals of compact sets
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {6},
     year = {2004},
     pages = {1877-1911},
     doi = {10.5802/aif.2070},
     zbl = {1071.03034},
     mrnumber = {2134228},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIF_2004__54_6_1877_0/

[1] J.P.R. Christensen Topology and Borel Structure, North-Holland/Elsevier (1974) | MR 348724 | Zbl 0273.28001

[2] I. Farah Analytic Quotients, Mem. Amer. Math. Soc, Tome 148 (2000) no. 702 | MR 1711328 | Zbl 0966.03045

[3] D.H. Fremlin The partially ordered sets of measure theory and Tukey's ordering, Note di Matematica, Tome 11 (1991), pp. 177-214 | MR 1258546 | Zbl 0799.06004

[4] D.H. Fremlin Families of compact sets and Tukey ordering, Atti. Sem. Mat. Fiz, Tome 39 (1991), pp. 29-50 | MR 1111757 | Zbl 0772.54030

[5] J.R. Isbell Seven cofinal types, J. London Math. Soc, Tome 4 (1972), pp. 651-654 | MR 294185 | Zbl 0238.06001

[6] A.S. Kechris Classical Descriptive Set Theory, Springer (1995) | MR 1321597 | Zbl 0819.04002

[7] A.S. Kechris; A. Louveau; W.H. Woodin The structure of σ-ideals of compact sets, Trans. Amer. Math. Soc, Tome 301 (1987), pp. 263-288 | MR 879573 | Zbl 0633.03043

[8] A. Louveau; B. Veli{#X010D;}Kovi{#X0107;} Analytic ideals and cofinal types, Ann. Pure Appl. Logic, Tome 99 (1999), pp. 171-195 | MR 1708151 | Zbl 0934.03061

[9] S. Solecki Analytic ideals and their applications, Ann. Pure Appl. Logic, Tome 99 (1999), pp. 51-72 | MR 1708146 | Zbl 0932.03060

[10] S. Todorcevic Directed sets and cofinal types, Trans. Amer. Math. Soc, Tome 290 (1985), pp. 711-723 | MR 792822 | Zbl 0592.03037

[11] S. Todorcevic A classification of transitive relations on 1 , Proc. London Math. Soc., Tome 73 (1996), pp. 501-533 | MR 1407459 | Zbl 0870.04001

[12] S. Todorcevic Analytic gaps, Fund. Math, Tome 150 (1996), pp. 55-66 | MR 1387957 | Zbl 0851.04002

[13] S. Todorcevic Definable ideals and gaps in their quotients, Set Theory (Curacao 1995, Barcelona, 1990), Kluwer, Dordrecht (1998), pp. 213-226 | MR 1602013 | Zbl 0894.03026

[14] J.W. Tukey Convergence and uniformity in topology, Princeton U.P, Ann. Math. Studies, Tome 1 (1940) | JFM 66.0961.01 | MR 2515 | Zbl 0025.09102

[15] S. Zafrany On analytic filters and prefilters, J. Symb. Logic, Tome 55 (1990), pp. 315-322 | MR 1043560 | Zbl 0705.03027