Authors: Todorčević, Stevo 
Xiao, M.
Title: A Borel chain condition of T(X)
Journal: Acta Mathematica Hungarica
Volume: 160
Issue: 2
First page: 314
Last page: 319
Issue Date: 1-Apr-2020
Rank: M23
ISSN: 0236-5294
DOI: 10.1007/s10474-019-00977-8
Abstract: 
We examine the Borel version of the σ-finite chain condition ofHorn and Tarski for a class of posets T(X) which have been used in the solutionof their well-known problem. More precisely, we show that the poset T(πQ) doesnot have the σ-finite chain condition witnessed by Borel pieces. More precisely,we define a condition on the topological spaces X under which the correspondingTodorcevic ordering T(X) does not have the σ-bounded chain condition witnessedby a countable Borel decomposition although it might satisfy the σ-finite chaincondition witnessed by a non Borel decomposition.
Keywords: Boolean algebra | chain condition
Publisher: Springer Link
Project: Natural Sciences and Engineering Research Council of Canada, Grant 455916

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