We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.

中文翻译：

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钻石、密实度和测量序列

我们在满足强同时反射性质的基数[公式：见正文]上建立了菱形原理失败的一致性。该结果基于对 Radin 强迫的分析，并进一步导致在 Radin 泛型扩展中 [Formula: see text] 的弱紧致性特征。