We investigate the interaction between compactness principles and guessing principles in the Radin forcing extensions. In particular, we show that in any Radin forcing extension with respect to a measure sequence on $\kappa$, if $\kappa$ is weakly compact, then $♢(\kappa )$ holds. This provides contrast with a well-known theorem of Woodin, who showed that in a certain Radin extension over a suitably prepared ground model relative to the existence of large cardinals, the diamond principle fails at a strongly inaccessible Mahlo cardinal. Refining the analysis of the Radin extensions, we consistently demonstrate a scenario where a compactness principle, stronger than the diagonal stationary reflection principle, holds yet the diamond principle fails at a strongly inaccessible cardinal, improving a result from [O. B. -Neria, Diamonds, compactness, and measure sequences, J. Math. Log. 19(1) (2019) 1950002].

我们研究了 Radin 强制扩展中紧凑性原则和猜测原则之间的相互作用。特别地，我们表明在任何 Radin 中关于测量序列的强制扩展$\kappa$， 如果$\kappa$是弱紧致的，那么$♢(\kappa )$持有。这与著名的 Woodin 定理形成对比，Woodin 表明在相对于大基数存在的适当准备的地面模型上的某个 Radin 扩展中，菱形原理在难以接近的 Mahlo 基数处失效。改进对 Radin 扩展的分析，我们始终如一地展示了一种场景，其中紧凑性原理比对角固定反射原理更强，但菱形原理在难以接近的基数处失败，改进了 [OB -Neria，Diamonds，紧凑性的结果和测量序列，J. Math。日志。19 (1) (2019) 1950002]。