We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a (non necessarily normal) ideal J extending the nonstationary ideal on a regular uncountable (non necessarily successor) cardinal \(\kappa \), our goal being to witness the nonsaturation of J by the existence of towers (of length possibly greater than \(\kappa ^+\)).

中文翻译：

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塔和俱乐部

我们重新审视了关于俱乐部原则和非平稳理想的非饱和性的一些结果，试图以各种方式对其进行改进。因此，我们通常处理（非必然正常）的理想Ĵ延长定期不可数的非平稳理想的（非必然的继任者）基数\（\卡帕\） ，我们的目标是见证的nonsaturation Ĵ通过塔的存在（的长度可能大于\（\ kappa ^ + \））。