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Finite basis for analytic multiple gaps

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Abstract

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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain

    Antonio Avilés

  2. Department of Mathematics, University of Toronto, Toronto, M5S 3G3, Canada

    Stevo Todorcevic

  3. Institut de Mathématiques de Jussieu, CNRS UMR 7586, Case 247, 4 place Jussieu, 75252, Paris Cedex, France

    Stevo Todorcevic

Authors
  1. Antonio Avilés
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  2. Stevo Todorcevic
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Correspondence to Stevo Todorcevic.

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Avilés, A., Todorcevic, S. Finite basis for analytic multiple gaps. Publ.math.IHES 121, 57–79 (2015). https://doi.org/10.1007/s10240-014-0063-8

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  • DOI: https://doi.org/10.1007/s10240-014-0063-8

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