|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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