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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