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},
     doi = {10.1007/s10240-014-0063-8},
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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. https://www.numdam.org/articles/10.1007/s10240-014-0063-8/

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