We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ${\omega }_1$ ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

中文翻译：

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关于相互平稳性与紧密平稳性的关系

我们构建了一个模型，其中每个正弦基数的每个增加的ω-序列都带有一个相互不固定的序列，该序列不是紧密固定的，并表明该性质在一类Prikry型强迫下得以保留。在此过程中，我们在Cohen和Prikry模型中给出了常规基数的ω-序列的示例，其中存在由紧定性组成的平稳子集的非紧密平稳序列${\omega }_{\mathrm{1个}}$ 序，并表明这种交错序列在交错的超紧凑基数存在下是相互固定的。