Finite basis for analytic multiple gaps
Avilés, Antonio1 ; Todorcevic, Stevo2, 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.

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
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 
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     title = {Finite basis for analytic multiple gaps},
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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://archive.numdam.org/articles/10.1007/s10240-014-0063-8/

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