$F_σ$理想之间的Tukey序
Tukey order among $F_σ$ ideals
摘要：
研究了$ω$的子集的$F_σ$理想类中的Tukey序.我们证明了没有非平凡的$F_σ$理想是Tukey低于一个$G_δ$理想的紧集。我们引入平坦理想和逐渐平坦理想的概念。我们证明了一个二分法定理平坦的理想隔离逐渐平坦的二分法，是结构上好的一面。我们使用Tukey约化和对策给出了平坦理想中的渐进平坦性的各种刻画。例如，我们表明，逐渐平坦的理想正是那些平坦的理想，Tukey低于理想的密度零集。
英文摘要：
We investigate the Tukey order in the class of $F_σ$ ideals of subsets of $ω$. We show that no nontrivial $F_σ$ ideal is Tukey below a $G_δ$ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and games. For example, we show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets.
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