Finite basis for analytic multiple gaps

Avilés, Antonio; Todorcevic, Stevo

doi:10.1007/s10240-014-0063-8

Avilés, Antonio ¹ ; Todorcevic, Stevo ^2,³

¹ Departamento de Matemáticas, Universidad de Murcia Campus de Espinardo 30100 Murcia Spain
² Department of Mathematics, University of Toronto M5S 3G3 Toronto Canada
³ Institut de Mathématiques de Jussieu, CNRS UMR 7586 Case 247, 4 place Jussieu 75252 Paris Cedex France

Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 57-79.

Résumé

An n-gap consists of n many pairwise orthogonal families of subsets of a countable set that cannot be separated. We prove that for every positive integer n there is a finite basis for the class of analytic n-gaps. The proof requires an analysis of certain combinatorial problems on the n-adic tree, and in particular a new partition theorem for trees.

DOI : 10.1007/s10240-014-0063-8

Mots clés : Winning Strategy, Finite Basis, Partition Theorem, Minimal Idempotent, Asymmetric Version

Affiliations des auteurs :

Avilés, Antonio ¹ ; Todorcevic, Stevo ^{2, 3}

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     author = {Avil\'es, Antonio and Todorcevic, Stevo},
     title = {Finite basis for analytic multiple gaps},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {57--79},
     publisher = {Springer Berlin Heidelberg},
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     year = {2015},
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Avilés, Antonio; Todorcevic, Stevo. Finite basis for analytic multiple gaps. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 57-79. doi : 10.1007/s10240-014-0063-8. http://www.numdam.org/articles/10.1007/s10240-014-0063-8/

Bibliographie
Cité par

[1.] Argyros, A. S.; Dodos, P.; Kanellopoulos, V. Unconditional families in Banach spaces, Math. Ann., Volume 341 (2008), pp. 15-38 | DOI | MR | Zbl

[2.] Avilés, A.; Todorcevic, S. Multiple gaps, Fundam. Math., Volume 213 (2011), pp. 15-42 | DOI | Zbl

[3.] Avilés, A.; Todorcevic, S. Finite basis for analytic strong n-gaps, Combinatorica, Volume 33 (2013), pp. 375-393 | DOI | MR | Zbl

[4.] Carlson, T. J.; Simpson, S. G. A dual form of Ramsey’s theorem, Adv. Math., Volume 53 (1984), pp. 265-290 | DOI | MR | Zbl

[5.] Dales, G. A discontinuous homomorphism from C(X), Am. J. Math., Volume 101 (1979), pp. 647-734 | DOI | MR | Zbl

[6.] Dales, H. G.; Woodin, W. H. An Introduction to Independence for Analysts (1987) (xiv+241 pp.) | DOI | Zbl

[7.] Dodos, P. Operators whose dual has non-separable range, J. Funct. Anal., Volume 260 (2011), pp. 1285-1303 | DOI | MR | Zbl

[8.] Dodos, P.; Kanellopoulos, V. On pair of definable orthogonal families, Ill. J. Math., Volume 52 (2008), pp. 181-201 | MR | Zbl

[9.] du Bois-Reymond, P. Eine neue Theorie der Convergenz und Divergenz von Reihen mitpositiven Gliedern, J. Reine Angew. Math., Volume 76 (1873), pp. 61-91 | DOI | Zbl

[10.] Esterle, J. Injection de semi-groupes divisibles dans des algèbres de convolution et construction d’homomorphismes discontinus de C(K), Proc. Lond. Math. Soc. (3), Volume 36 (1978), pp. 59-85 | DOI | MR | Zbl

[11.] Gowers, W. T. Lipschitz functions on classical spaces, Eur. J. Comb., Volume 13 (1992), pp. 141-151 | DOI | MR | Zbl

[12.] Hadamard, J. Sur les caractères de convergence des séries à termes positifs et sur les fonctions indéfiniment croissantes, Acta Math., Volume 18 (1894), pp. 319-336 | DOI | MR | Zbl

[13.] Hales, A. W.; Jewett, R. I. Regularity and positional games, Trans. Am. Math. Soc., Volume 106 (1963), pp. 222-229 | DOI | MR | Zbl

[14.] Hausdorff, F. Die Graduierung nach dem Endverlauf, Abh. Königl. Sächs. Gesell. Wiss. Math.-Phys. Kl., Volume 31 (1909), pp. 296-334

[15.] Hausdorff, F. Summen von ℵ₁ Mengen, Fundam. Math., Volume 26 (1936), pp. 241-255

[16.] Kaplansky, I. Normed algebras, Duke Math. J., Volume 16 (1949), pp. 399-418 | DOI | MR | Zbl

[17.] Kechris, A. Classical Descriptive Set Theory (1995) | Zbl

[18.] Milliken, K. R. A partition theorem for the infinite subtrees of a tree, Trans. Am. Math. Soc., Volume 263 (1981), pp. 137-148 | DOI | MR | Zbl

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

[20.] Todorcevic, S. Compact subsets of the first Baire class, J. Am. Math. Soc., Volume 12 (1999), pp. 1179-1212 | DOI | MR | Zbl

[21.] Todorcevic, S. Introduction to Ramsey Spaces (2010) | DOI

[22.] Woodin, W. H. On the consistency strength of projective uniformization, Proceedings of Herbrand Symposium (1982), pp. 365-384 | DOI

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