集合论讨论班报告 报告人：Mr. Ming Xiao（University of Toronto） 时间：8月13日14:00-16:00 地点：南楼N902 题目：A Borel Chain Condition of T(X) 摘要：In 1948, Horn and Tarski conjectured whether the $\sigma$-finite chain condition and $\sigma$-bounded chain condition are equivalent. The first counter example was given by Thummel in 2012 and then a Borel counter example was given by Todorvevic in 2014. Both examples belong to a class of poset called "Todorvevic ordering" $T(X)$ over topological spaces $X$. In this talk, I will illustrate a satisfactory condition for a topological space $X$ making the corresponding poset $T(X)$ fail to have a countable Borel partition witenessing the $\sigma$ finite chain condition , although it may still witnessed by non Borel partitions.
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