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A Borel chain condition of T(X)

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Abstract

We examine the Borel version of the \(\sigma \)-finite chain condition of Horn and Tarski for a class of posets T(X) which have been used in the solution of their well-known problem. More precisely, we show that the poset \(T(\pi \mathbb{Q} \it )\) does not have the \(\sigma \)-finite chain condition witnessed by Borel pieces. More precisely, we define a condition on the topological spaces X under which the corresponding Todorcevic ordering T(X) does not have the \(\sigma \)-bounded chain condition witnessed by a countable Borel decomposition although it might satisfy the \(\sigma \)-finite chain condition witnessed by a non Borel decomposition.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada

    S. Todorcevic & M. Xiao

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  1. S. Todorcevic
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  2. M. Xiao
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Correspondence to M. Xiao.

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Partially supported by NSERC grant (455916).

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Todorcevic, S., Xiao, M. A Borel chain condition of T(X). Acta Math. Hungar. 160, 314–319 (2020). https://doi.org/10.1007/s10474-019-00977-8

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  • DOI: https://doi.org/10.1007/s10474-019-00977-8

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