Authors: Avilés, Antonio
Todorčević, Stevo 
Title: Finite basis for analytic multiple gaps
Journal: Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume: 121
Issue: 1
First page: 57
Last page: 79
Issue Date: 27-Jun-2015
Rank: M21a
ISSN: 0073-8301
DOI: 10.1007/s10240-014-0063-8
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.
Publisher: Springer Link

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