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Finite basis for analytic multiple gaps
Antonio Avilés1 ; Stevo Todorcevic2, 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, Volume 121 (2015), pp. 57-79
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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.

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DOI: 10.1007/s10240-014-0063-8
Keywords: Winning Strategy, Finite Basis, Partition Theorem, Minimal Idempotent, Asymmetric Version

Antonio Avilés 1; Stevo Todorcevic 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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Antonio Avilés; Stevo Todorcevic. Finite basis for analytic multiple gaps. Publications Mathématiques de l'IHÉS, Volume 121 (2015), pp. 57-79. doi: 10.1007/s10240-014-0063-8

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