We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak {s}_\theta , \mathfrak {p}_\theta , \mathfrak {t}_\theta , \mathfrak {g}_\theta , \mathfrak {r}_\theta $ at uncountable regular cardinals $\theta $ . Motivated by a theorem of Raghavan–Shelah who proved that $\mathfrak {s}_\theta \leq \mathfrak {b}_\theta $ , we explore in the first part of the paper the consistency of inequalities comparing $\mathfrak {s}_\theta $ with $\mathfrak {p}_\theta $ and $\mathfrak {g}_\theta $ . In the second part of the paper we study variations of the extender-based Radin forcing to establish several consistency results concerning $\mathfrak {r}_\theta ,\mathfrak {s}_\theta $ from hyper-measurability assumptions, results which were previously known to be consistent only from supercompactness assumptions. In doing so, we answer questions from [1], [15] and [7], and improve the large cardinal strength assumptions for results from [10] and [3].

中文翻译：

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关于常规红衣主教的红衣主教特征的配置

我们研究了关于基本特征的各种配置的一致性和一致性强度$\mathfrak {s}_\theta , \mathfrak {p}_\theta , \mathfrak {t}_\theta , \mathfrak {g}_\theta , \mathfrak {r}_\theta $在不可数的常规红衣主教$\θ$. 受到 Raghavan-Shelah 定理的启发，他证明了$\mathfrak {s}_\theta \leq \mathfrak {b}_\theta $，我们在论文的第一部分探讨了不等式比较的一致性$\mathfrak {s}_\theta $和$\mathfrak {p}_\theta $和$\mathfrak {g}_\theta $. 在本文的第二部分，我们研究了基于扩展器的 Radin 强迫的变化，以建立几个关于以下方面的一致性结果$\mathfrak {r}_\theta ,\mathfrak {s}_\theta $来自超可测量性假设，以前已知的结果仅与超紧致性假设一致。在这样做的过程中，我们回答了来自 [1]、[15] 和 [7] 的问题，并改进了来自 [10] 和 [3] 的结果的大基数强度假设。