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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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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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