论文标题
$f_σ$理想中的tukey订单
Tukey order among $F_σ$ ideals
论文作者
论文摘要
我们研究了$f_σ$ $ω$的$f_σ$理想的Tukey订单。我们表明，没有非平凡的$f_σ$理想的理想是$g_Δ$紧凑型套件的理想。我们介绍了平坦的理想和逐渐平坦的理想的概念。我们证明了一种二分法定理，用于平坦的理想分离逐渐平坦的二分法一侧，在结构上是良好的。我们使用Tukey减少和游戏对平坦理想的逐渐平坦度进行了多样化的特征。例如，我们表明，逐渐平坦的理想是那些平坦的理想，这些理想是低于密度零集的理想的那些平坦的理想。
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.
