Abstract Under Martin Axiom, we prove that for each ordinal γ ω 1 there exists a thin ultrafilter that belongs to the class P γ of the P-hierarchy of ultrafilters. Since the class P 2 of ultrafilters coincides with the class of P-points, this result generalizes a theorem of Flaskova, which states that, under the Martin Axiom for countable posets, there exists a thin ultrafilter which is not a P-point. It is also related to a theorem which states that, under Continuum Hypothesis, for any tall P-ideal I on ω there are I -ultrafilters in each class P γ of the P-hierarchy. However, the ideal of thin sets is not a P-ideal.

中文翻译：

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薄超滤器和超滤器的 P 层级

摘要 在马丁公理下，我们证明对于每个序数 γ ω 1 都存在一个薄超滤器，它属于超滤器 P 层级的 P γ 类。由于超滤器的 P 2 类与 P 点的类重合，该结果推广了 Flaskova 定理，该定理指出，在可数偏序组的马丁公理下，存在一个不是 P 点的薄超滤器。它也与一个定理有关，该定理指出，在连续统假设下，对于 ω 上的任何高 P 理想 I，在 P 层次结构的每个类 P γ 中都有 I 超滤波器。然而，瘦集的理想不是 P 理想。