In this paper, we study some new examples of ideals on \(\omega \) with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is an analytic P-ideal above all other analytic P-ideals in the weak Rudin–Keisler order.

中文翻译：

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最大 Tukey 类型、P 理想和弱 Rudin-Keisler 阶

在本文中，我们研究了具有最大 Tukey 类型（即尺寸连续体的偏序中的最大值）的\(\omega \)上理想的一些新例子。接下来的讨论将深入研究 Tukey 阶的改进（称为弱 Rudin-Keisler 阶）及其在限制为最大 Tukey 类型理想时的结构。反映 Fremlin (Note Mat 11:177–214, 1991) 在 Tukey 阶上的结果，我们还表明在弱 Rudin–Keisler 阶中存在一个高于所有其他解析 P 理想的解析 P 理想。