中科院数学与系统科学研究院
数学研究所
集合论研讨班报告
报告人：何家亮（四川大学）
题 目：Tukey order among F_sigma ideal
时 间：2021.03.19（星期五）, 13:30-15:30
地 点：思源楼S805
摘 要：In this talk, we will investigate the Tukey order in the class of F_sigma ideals of subsets of N and show that no nontrivial F_sigma ideal is Tukey below a G_delta sigma-ideal of compact sets.
We will also introduce the notions of flat ideals and gradually flat ideals. We will prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We will give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, all gradually flat ideals are Tukey below the density zero ideal mathcal Z_0.
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